Turbulent Heat Exchanger

Author COMSOL Date 20 Apr, 2012 2:18:00 PM

SummaryIn this model you study a part of a shell-and-tube heat exchanger using the k- turbulence model to model the fully developed turbulent flow.

1

Contents1. Global Definitions............................................................................................................................. 3 1.1. Parameters 1 ............................................................................................................................ 3 2. Model 1 (mod1) ............................................................................................................................... 4 2.1. Definitions ................................................................................................................................ 4 2.2. Geometry 1 .............................................................................................................................. 4 2.3. Materials .................................................................................................................................. 6 2.4. Non - Isothermal Flow (nitf) ................................................................................................... 11 2.5. Mesh 1.................................................................................................................................... 68 3. Study 1 ........................................................................................................................................... 70 3.1. Stationary ............................................................................................................................... 70 3.2. Solver Configurations ............................................................................................................. 70 4. Results ............................................................................................................................................ 87 4.1. Data Sets ................................................................................................................................ 87 4.2. Plot Groups ............................................................................................................................ 88

2

1 Global Definitions1.1 Parameters 1Parameters

Name T_in

Expression Description 323[K] Inflow temperature Pipe temperature Inflow velocity

T_pipe 278[K] v_in -1.5[m/s]

3

2 Model 1 (mod1)2.1 Definitions2.1.1 Coordinate Systems

Boundary System 1 Coordinate system type Boundary system IdentifierSettings

sys1

Name Coordinate names

Value {t1, n, to}

Create first tangent direction from Global Cartesian

2.2 Geometry 1

Geometry 1 units

Length unit

mm

Angular unit degGeometry statistics

Property Space dimension Number of domains

Value 2 40 4

Property

Value

Number of boundaries 172 2.2.1Position

Rectangle 1 (r1) Value

Name

Position {0, 0} Width Height Size 2.2.2Position

50 100 {50, 100} Circle 1 (c1) Value

Name

Position {0, 0} Radius 2.2.3Position

27.5 Circle 2 (c2) Value

Name

Position {0, 0} Radius 2.2.4 Name 25 Copy 1 (copy1) Value

Selections of resulting entities

Keep input objects On x y 2.2.5 Name 0 100 Copy 2 (copy2) Value

Selections of resulting entities

Keep input objects On x y 50 50 5

2.2.6 Name

Array 1 (arr1) Value Linear 10

Selections of resulting entities

Array type Size

Displacement {0, 100}

2.3 Materials2.3.1 Steel AISI 4340

Steel AISI 4340 Selection

Geometric entity level Selection

Domain Domains 1, 34, 67, 910, 1213, 1516, 1819, 2122, 2425, 2728, 3040

Material parameters

Name

Value

Unit J/(kg*K) kg/m^3

Heat capacity at constant pressure 475[J/(kg*K)] Density Thermal conductivityBasic Settings

7850[kg/m^3]

44.5[W/(m*K)] W/(m*K)

Description

Value 6

Description Relative permeability Electrical conductivity Coefficient of thermal expansion Heat capacity at constant pressure Relative permittivity Density Thermal conductivity

Value {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}} {{4.032e6[S/m], 0, 0}, {0, 4.032e6[S/m], 0}, {0, 0, 4.032e6[S/m]}} {{12.3e6[1/K], 0, 0}, {0, 12.3e6[1/K], 0}, {0, 0, 12.3e6[1/K]}} 475[J/(kg*K)] {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}} 7850[kg/m^3] {{44.5[W/(m*K)], 0, 0}, {0, 44.5[W/(m*K)], 0}, {0, 0, 44.5[W/(m*K)]}}

Young's modulus and Poisson's ratio Settings

Description

Value

Young's modulus 205e9[Pa] Poisson's ratio 2.3.2 0.28

Water, liquid

Water, liquid Selection

Geometric entity level Domain SelectionMaterial parameters

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

7

Name Dynamic viscosity Ratio of specific heats

Value eta(T[1/K])[Pa*s] 1.0

Unit Pa*s 1 J/(kg*K)

Heat capacity at constant pressure Cp(T[1/K])[J/(kg*K)] Density Thermal conductivityBasic Settings

rho(T[1/K])[kg/m^3] kg/m^3 k(T[1/K])[W/(m*K)] W/(m*K)

Description Dynamic viscosity Ratio of specific heats Electrical conductivity Heat capacity at constant pressure Density Thermal conductivity Speed of soundFunctions

Value eta(T[1/K])[Pa*s] 1.0 {{5.5e6[S/m], 0, 0}, {0, 5.5e6[S/m], 0}, {0, 0, 5.5e6[S/m]}} Cp(T[1/K])[J/(kg*K)] rho(T[1/K])[kg/m^3] {{k(T[1/K])[W/(m*K)], 0, 0}, {0, k(T[1/K])[W/(m*K)], 0}, {0, 0, k(T[1/K])[W/(m*K)]}} cs(T[1/K])[m/s]

Function name Type eta Cp rho k cs Piecewise Piecewise Piecewise Piecewise Interpolation

8

eta

Cp

9

rho

k

10

cs

2.4 Non-Isothermal Flow (nitf)

Non-Isothermal Flow Selection

Geometric entity level Domain SelectionEquations

Domains 140

11

Settings

Description Turbulence model type

Value RANS

Use pseudo time stepping for stationary equation form 1 Show equation assumingUsed products

std1/stat

COMSOL Multiphysics Heat Transfer Module 2.4.1 Fluid 1

Fluid 1 Selection

12

Geometric entity level Domain Selection Equations Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

Properties from material

Property Density Dynamic viscosity Thermal conductivity

Material

Property group

Water, liquid Basic Water, liquid Basic Water, liquid Basic

Heat capacity at constant pressure Water, liquid Basic Ratio of specific heats Variables Name nitf.rho Expression model.input.rho Unit kg/m^3 Description Density Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Water, liquid Basic

nitf.fluid1.minput_te model.input.minput_te mperature mperature nitf.mu model.input.mu

K

Temperature

Pa*s

Dynamic viscosity

nitf.divu

ux + vy

1/s

Divergence of velocity field Shear rate

nitf.sr

sqrt(0.5*(4*ux^2 + 2*(uy + vx)^2 + 4*vy^2) + eps)

1/s

13

Name nitf.Fx

Expression 0

Unit N/m^3

Description Volume force, x component Volume force, y component Volume force, z component Velocity magnitude

Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127,

nitf.Fy

0

N/m^3

nitf.Fz

0

N/m^3

nitf.U

sqrt(u^2 + v^2)

m/s

nitf.vorticityx

0

1/s

Vorticity field, x component Vorticity field, y component Vorticity field, z component Vorticity magnitude

nitf.vorticityy

0

1/s

nitf.vorticityz

vx - uy

1/s

nitf.vort_magn

sqrt(nitf.vorticityx^2 + nitf.vorticityy^2 + nitf.vorticityz^2)

1/s

nitf.cellRe

0.25*nitf.rho*sqrt(u^2 + 1 v^2)*h/nitf.mu nitf.mu/nitf.rho m^2/s

Cell Reynolds number Kinematic viscosity

nitf.nu

nitf.betaT

d(nitf.rho, p)/nitf.rho

1/Pa

Isothermal compressibility coefficient Total stress, x component

nitf.T_stressx

2*(nitf.mu + N/m^2 nitf.muT)*ux*nitf.nxme sh + (nitf.mu + nitf.muT)*(uy + vx)*nitf.nymesh 2*nitf.divu*(nitf.mu + nitf.muT)*nitf.nxmesh/3 - p*nitf.nxmesh 2*up(nitf.rho)*k*nitf.nx 14

Name

Expression mesh/3

Unit

Description

Selection 130131, 133152

nitf.T_stressy

(nitf.mu + nitf.muT)*(vx N/m^2 + uy)*nitf.nxmesh + 2*(nitf.mu + nitf.muT)*vy*nitf.nymes h - 2*nitf.divu*(nitf.mu + nitf.muT)*nitf.nymesh/ 3 - p*nitf.nymesh 2*up(nitf.rho)*k*nitf.ny mesh/3 nitf.nzmesh*(2*nitf.divu N/m^2 *(nitf.mu + nitf.muT)/3 p - 2*up(nitf.rho)*k/3)

Total stress, y component

Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 42, 52 53, 5657, 6061, 64 65, 6869, 7273, 76 77, 8081, 8485, 88 89, 92 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 42, 52 53, 5657, 6061, 64 65, 6869, 7273, 76 77, 8081, 8485, 88

nitf.T_stressz

Total stress, z component

nitf.T_stressx

2*(nitf.mu + N/m^2 nitf.muT)*ux*nitf.nxme sh + (nitf.mu + nitf.muT)*(uy + vx)*nitf.nymesh 2*nitf.divu*(nitf.mu + nitf.muT)*nitf.nxmesh/3 - p*nitf.nxmesh 2*down(nitf.rho)*k*nitf .nxmesh/3 (nitf.mu + nitf.muT)*(vx N/m^2 + uy)*nitf.nxmesh + 2*(nitf.mu + nitf.muT)*vy*nitf.nymes h - 2*nitf.divu*(nitf.mu + nitf.muT)*nitf.nymesh/ 3 - p*nitf.nymesh 2*down(nitf.rho)*k*nitf 15

Total stress, x component

nitf.T_stressy

Total stress, y component

Name

Expression .nymesh/3

Unit

Description

Selection 89, 92

nitf.T_stressz

nitf.nzmesh*(2*nitf.divu N/m^2 *(nitf.mu + nitf.muT)/3 p2*down(nitf.rho)*k/3)

Total stress, z component

Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 42, 52 53, 5657, 6061, 64 65, 6869, 7273, 76 77, 8081, 8485, 88 89, 92 Boundaries 4351

nitf.T_stressx

2*(nitf.mu + N/m^2 nitf.muT)*ux*nitf.nxme sh + (nitf.mu + nitf.muT)*(uy + vx)*nitf.nymesh 2*nitf.divu*(nitf.mu + nitf.muT)*nitf.nxmesh/3 - p*nitf.nxmesh 2*nitf.rho*k*nitf.nxmes h/3 (nitf.mu + nitf.muT)*(vx N/m^2 + uy)*nitf.nxmesh + 2*(nitf.mu + nitf.muT)*vy*nitf.nymes h - 2*nitf.divu*(nitf.mu + nitf.muT)*nitf.nymesh/ 3 - p*nitf.nymesh 2*nitf.rho*k*nitf.nymes h/3 nitf.nzmesh*(2*nitf.divu N/m^2 *(nitf.mu + nitf.muT)/3 p - 2*nitf.rho*k/3) (nitf.mu + nitf.muT)*(2*ux*nitf.nx mesh + (uy + vx)*nitf.nymesh 2*nitf.divu*nitf.nxmesh /3) N/m^2

Total stress, x component

nitf.T_stressy

Total stress, y component

Boundaries 4351

nitf.T_stressz

Total stress, z component Viscous stress, x component

Boundaries 4351 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84

nitf.K_stressx

16

Name

Expression

Unit

Description

Selection 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152

nitf.K_stressy

(nitf.mu + nitf.muT)*((vx N/m^2 + uy)*nitf.nxmesh + 2*vy*nitf.nymesh 2*nitf.divu*nitf.nymesh /3)

Viscous stress, y component

Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114

nitf.K_stressz

-2*nitf.divu*(nitf.mu + nitf.muT)*nitf.nzmesh/3

N/m^2

Viscous stress, z component

17

Name

Expression

Unit

Description

Selection 115, 118 119, 122 123, 126 127, 130 131, 133152

nitf.upwind_helpx

u

m/s

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Viscous stress tensor, xx component Viscous stress tensor, yx component Viscous stress tensor, zx component Viscous stress tensor, xy component Viscous stress tensor, yy component Viscous stress tensor, zy component Viscous stress tensor, xz component Viscous stress tensor, yz component Viscous stress tensor, zz component Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.upwind_helpy

v

m/s

nitf.upwind_helpz

0

m/s

nitf.K_stress_tensor xx nitf.K_stress_tensor yx nitf.K_stress_tensor zx nitf.K_stress_tensor xy nitf.K_stress_tensor yy nitf.K_stress_tensor zy nitf.K_stress_tensor xz nitf.K_stress_tensor yz nitf.K_stress_tensor zz

(nitf.mu + nitf.muT)*(2*ux 2*nitf.divu/3) (nitf.mu + nitf.muT)*(vx + uy) 0

N/m^2

N/m^2

N/m^2

(nitf.mu + nitf.muT)*(uy + vx) (nitf.mu + nitf.muT)*(2*vy 2*nitf.divu/3) 0

N/m^2

N/m^2

N/m^2

0

N/m^2

0

N/m^2

-2*(nitf.mu + nitf.muT)*nitf.divu/3

N/m^2

18

Name nitf.K_stress_tensor _testxx nitf.K_stress_tensor _testyx nitf.K_stress_tensor _testzx nitf.K_stress_tensor _testxy nitf.K_stress_tensor _testyy nitf.K_stress_tensor _testzy nitf.K_stress_tensor _testxz nitf.K_stress_tensor _testyz nitf.K_stress_tensor _testzz nitf.res_k

Expression (nitf.mu + nitf.muT)*(2*test(ux) 2*(test(ux) + test(vy))/3) (nitf.mu + nitf.muT)*(test(vx) + test(uy)) 0

Unit N/m^2

Description Viscous stress tensor test, xx component Viscous stress tensor test, yx component Viscous stress tensor test, zx component Viscous stress tensor test, xy component Viscous stress tensor test, yy component Viscous stress tensor test, zy component Viscous stress tensor test, xz component Viscous stress tensor test, yz component Viscous stress tensor test, zz component Turbulent kinetic energy equation residual

Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

N/m^2

N/m^2

(nitf.mu + nitf.muT)*(test(uy) + test(vx)) (nitf.mu + nitf.muT)*(2*test(vy) 2*(test(ux) + test(vy))/3) 0

N/m^2

N/m^2

N/m^2

0

N/m^2

0

N/m^2

-2*(nitf.mu + nitf.muT)*(test(ux) + test(vy))/3 -(nitf.mu + nitf.muT/nitf.sigmak)*(d (kx, x) + d(ky, y)) + nitf.rho*(2*(ux + vy)/3 + nitf.gammaT)*k - nitf.Pk + nitf.rho*u*kx + nitf.rho*v*ky

N/m^2

W/m^3

nitf.res_ep

-(nitf.mu + Pa/s^2 nitf.muT/nitf.sigmaeps) *(d(epx, x) + d(epy, y)) + nitf.Ceps2*nitf.rho*nitf. gammaT*ep + 2*nitf.Ceps1*nitf.rho*(u x + vy)*ep/3 + nitf.rho*u*epx + 19

Turbulent dissipation Domains 2, 5, rate equation 8, 11, 14, 17, residual 20, 23, 26, 29

Name

Expression nitf.rho*v*epy nitf.Ceps1*nitf.gammaT *nitf.Pk

Unit

Description

Selection

nitf.alphap

-d(nitf.rho, T)/(nitf.rho + eps) 1[atm]

1/K

Isobaric compressibility coefficient Absolute pressure

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.pA

Pa

nitf.ux

model.input.minput_vel ocity1 model.input.minput_vel ocity2 model.input.minput_vel ocity3 Tx

m/s

Velocity field, x component Velocity field, y component Velocity field, z component Temperature gradient, x component Temperature gradient, y component Temperature gradient, z component Temperature gradient magnitude Mean effective thermal conductivity

nitf.uy

m/s

nitf.uz

m/s

nitf.gradTx

K/m

nitf.gradTy

Ty

K/m

nitf.gradTz

0

K/m

nitf.gradTmag

sqrt(nitf.gradTx^2 + nitf.gradTy^2 + nitf.gradTz^2) 0.5*(root.mod1.nitf.k_e ff_p1 + root.mod1.nitf.k_eff_p2 ) -nitf.kappaT*Tx

K/m

nitf.kmean

W/(m*K)

nitf.turbfluxx

W/m^2

Turbulent heat flux, x component Turbulent heat flux, y component

nitf.turbfluxy

-nitf.kappaT*Ty

W/m^2

20

Name nitf.turbfluxz

Expression 0

Unit W/m^2

Description Turbulent heat flux, z component

Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.dfluxx

-nitf.k_effxx*Tx nitf.k_effxy*Ty -nitf.k_effyx*Tx nitf.k_effyy*Ty -nitf.k_effzx*Tx nitf.k_effzy*Ty sqrt(nitf.dfluxx^2 + nitf.dfluxy^2 + nitf.dfluxz^2) 0

W/m^2

Conductive heat flux, Domains 2, 5, x component 8, 11, 14, 17, 20, 23, 26, 29 Conductive heat flux, Domains 2, 5, y component 8, 11, 14, 17, 20, 23, 26, 29 Conductive heat flux, Domains 2, 5, z component 8, 11, 14, 17, 20, 23, 26, 29 Conductive heat flux magnitude Heat source Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.dfluxy

W/m^2

nitf.dfluxz

W/m^2

nitf.dfluxMag

W/m^2

nitf.Q

W/m^3

nitf.qs

0

W/(m^3*K)

Production/absorpti on coefficient Metabolic heat source Total heat source

nitf.Qmet

0

W/m^3

nitf.Qtot

0

W/m^3

nitf.rhoInt

nitf.rho

kg/m^3

Density for integration Specific heat capacity for integration Ratio of specific heats for integration Reference enthalpy

nitf.CpInt

nitf.Cp

J/(kg*K)

nitf.gammaInt

nitf.gamma

1

nitf.HRef

subst(subst(nitf.CpInt, nitf.pA, 1[atm]), T, 298.15[K])*298.15[K]/su bst(subst(nitf.gammaInt , nitf.pA, 1[atm]), T,

J/kg

21

Name

Expression 298.15[K]) + 1[atm]/subst(subst(nitf. rhoInt, nitf.pA, 1[atm]), T, 298.15[K])

Unit

Description

Selection

nitf.DeltaH

0.05*((subst(subst(nitf. CpInt, nitf.pA, 1[atm]), T, 298.15[K]) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.9*298.15[K] + 0.1*T) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.8*298.15[K] + 0.2*T) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.7*298.15[K] + 0.3*T) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.6*298.15[K] + 0.4*T) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.5*(298.15[K] + T)) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.4*298.15[K] + 0.6*T) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.30000000000000004* 298.15[K] + 0.7*T) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.19999999999999996* 298.15[K] + 0.8*T) + 2*subst(subst(nitf.CpInt , nitf.pA, 1[atm]), T, 0.09999999999999998* 298.15[K] + 0.9*T) + subst(nitf.CpInt, nitf.pA, 1[atm]))*(T - 298.15[K]) + (subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 1[atm]) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn

J/kg

Sensible enthalpy

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

22

Name

Expression t, nitf.pA, 0.9*1[atm] + 0.1*nitf.pA) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 0.8*1[atm] + 0.2*nitf.pA) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 0.7*1[atm] + 0.3*nitf.pA) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 0.6*1[atm] + 0.4*nitf.pA) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 0.5*(1[atm] + nitf.pA)) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 0.4*1[atm] + 0.6*nitf.pA) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 0.30000000000000004* 1[atm] + 0.7*nitf.pA) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 0.19999999999999996* 1[atm] + 0.8*nitf.pA) + 2*subst((1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn t, nitf.pA, 0.09999999999999998* 1[atm] + 0.9*nitf.pA) + (1 + T*d(nitf.rhoInt, T)/nitf.rhoInt)/nitf.rhoIn

Unit

Description

Selection

23

Name

Expression t)*(nitf.pA - 1[atm]))

Unit

Description

Selection

nitf.H

nitf.HRef + nitf.DeltaH

J/kg

Enthalpy

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.H0

nitf.H + 0.5*(nitf.ux^2 + nitf.uy^2 + nitf.uz^2) nitf.H - nitf.pA/nitf.rho

J/kg

Total enthalpy

nitf.Ei

J/kg

Internal energy

nitf.Ei0

nitf.Ei + 0.5*(nitf.ux^2 + nitf.uy^2 + nitf.uz^2) 0

J/kg

Total internal energy

nitf.trlfluxx

W/m^2

Translational heat flux, x component Translational heat flux, y component Translational heat flux, z component Convective heat flux, x component Convective heat flux, y component Convective heat flux, z component Total heat flux, x component Total heat flux, y component Total heat flux, z component

nitf.trlfluxy

0

W/m^2

nitf.trlfluxz

0

W/m^2

nitf.afluxx

nitf.rho*nitf.ux*nitf.Ei

W/m^2

nitf.afluxy

nitf.rho*nitf.uy*nitf.Ei

W/m^2

nitf.afluxz

nitf.rho*nitf.uz*nitf.Ei

W/m^2

nitf.tfluxx

nitf.dfluxx + nitf.trlfluxx + nitf.afluxx nitf.dfluxy + nitf.trlfluxy + nitf.afluxy nitf.dfluxz + nitf.trlfluxz + nitf.afluxz

W/m^2

nitf.tfluxy

W/m^2

nitf.tfluxz

W/m^2

24

Name nitf.tfluxMag

Expression sqrt(nitf.tfluxx^2 + nitf.tfluxy^2 + nitf.tfluxz^2) nitf.dfluxx + nitf.rho*nitf.ux*nitf.H0 nitf.dfluxy + nitf.rho*nitf.uy*nitf.H0 nitf.dfluxz + nitf.rho*nitf.uz*nitf.H0 sqrt(nitf.tefluxx^2 + nitf.tefluxy^2 + nitf.tefluxz^2) 0

Unit W/m^2

Description Total heat flux magnitude Total energy flux, x component Total energy flux, y component Total energy flux, z component Total energy flux magnitude Radiative heat flux

Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84

nitf.tefluxx

W/m^2

nitf.tefluxy

W/m^2

nitf.tefluxz

W/m^2

nitf.tefluxMag

W/m^2

nitf.rflux

W/m^2

nitf.ccflux

0

W/m^2

Convective heat flux

25

Name

Expression

Unit

Description

Selection 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152

nitf.ntrlflux

mean(nitf.trlfluxx)*nitf. nx + mean(nitf.trlfluxy)*nitf. ny + mean(nitf.trlfluxz)*nitf. nz

W/m^2

Normal translational heat flux

Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114

nitf.naflux

mean(nitf.afluxx)*nitf.n x+ mean(nitf.afluxy)*nitf.n y+ mean(nitf.afluxz)*nitf.n z

W/m^2

Normal convective heat flux

26

Name

Expression

Unit

Description

Selection 115, 118 119, 122 123, 126 127, 130 131, 133152

nitf.ndflux

mean(nitf.dfluxx)*nitf.n x+ mean(nitf.dfluxy)*nitf.n y+ mean(nitf.dfluxz)*nitf.n z

W/m^2

Normal conductive heat flux

Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152

nitf.ntflux

nitf.ndflux + nitf.ntrlflux + nitf.naflux

W/m^2

Total normal heat flux

27

Name nitf.nteflux

Expression

Unit

Description Total normal energy flux

Selection Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465, 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152 Boundaries 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 4253, 5657, 60 61, 6465,

mean(nitf.tefluxx)*nitf.n W/m^2 x+ mean(nitf.tefluxy)*nitf. ny + mean(nitf.tefluxz)*nitf.n z

nitf.Qbtot

0

W/m^2

Total boundary heat source

nitf.Qltot

0

W/m

Total heat source

28

Name

Expression

Unit

Description

Selection 6869, 72 73, 7677, 8081, 84 85, 8889, 92, 9495, 9899, 102 103, 106 107, 110 111, 114 115, 118 119, 122 123, 126 127, 130 131, 133152

nitf.res_T

-nitf.k_effxx*d(Tx, x) nitf.k_effxy*d(Tx, y) nitf.k_effyx*d(Ty, x) nitf.k_effyy*d(Ty, y) (nitf.qs + nitf.qs_oop)*T + nitf.rho*nitf.Cp*(nitf.ux *Tx + nitf.uy*Ty) - nitf.Q - nitf.Qoop 0.5*nitf.rho*nitf.Cp*h*s qrt(nitf.ux^2 + nitf.uy^2 + nitf.uz^2)/nitf.kmean sqrt((nitf.rho*nitf.ux*nit f.Ei)^2 + (nitf.rho*nitf.uy*nitf.Ei) ^2 + (nitf.rho*nitf.uz*nitf.Ei) ^2) model.input.k11

W/m^3

Equation residual

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.cellPe

1

Cell Pclet number

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.afluxMag

W/m^2

Convective heat flux magnitude

nitf.kxxht

W/(m*K)

Thermal conductivity, xx component Thermal conductivity, yx component Thermal conductivity, zx component Thermal conductivity, xy

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17,

nitf.kyxht

model.input.k21

W/(m*K)

nitf.kzxht

model.input.k31

W/(m*K)

nitf.kxyht

model.input.k12

W/(m*K)

29

Name

Expression

Unit

Description component

Selection 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.kyyht

model.input.k22

W/(m*K)

Thermal conductivity, yy component Thermal conductivity, zy component Thermal conductivity, xz component Thermal conductivity, yz component Thermal conductivity, zz component Effective thermal conductivity, xx component Effective thermal conductivity, yx component Effective thermal conductivity, zx component Effective thermal conductivity, xy component Effective thermal conductivity, yy component Effective thermal conductivity, zy component Effective thermal conductivity, xz component Effective thermal conductivity, yz component

nitf.kzyht

model.input.k32

W/(m*K)

nitf.kxzht

model.input.k13

W/(m*K)

nitf.kyzht

model.input.k23

W/(m*K)

nitf.kzzht

model.input.k33

W/(m*K)

nitf.k_effxx

nitf.kxxht + nitf.kappaT

W/(m*K)

nitf.k_effyx

nitf.kyxht

W/(m*K)

nitf.k_effzx

0

W/(m*K)

nitf.k_effxy

nitf.kxyht

W/(m*K)

nitf.k_effyy

nitf.kyyht + nitf.kappaT

W/(m*K)

nitf.k_effzy

0

W/(m*K)

nitf.k_effxz

0

W/(m*K)

nitf.k_effyz

0

W/(m*K)

30

Name nitf.k_effzz

Expression 0

Unit W/(m*K)

Description Effective thermal conductivity, zz component Effective volumetric heat capacity Speed of sound

Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.C_eff

nitf.rho*nitf.Cp

J/(m^3*K)

nitf.c_s

sqrt(nitf.gamma/max(su bst(d(nitf.rhoInt, nitf.pA), nitf.pA, root.mod1.nitf.fluid1.mi nput_pressure), eps)) sqrt(model.input.minpu t_velocity1^2 + model.input.minput_vel ocity2^2 + model.input.minput_vel ocity3^2)/sqrt(nitf.gam ma/max(subst(d(nitf.rh oInt, nitf.pA), nitf.pA, root.mod1.nitf.fluid1.mi nput_pressure), eps)) model.input.gamma

m/s

nitf.Ma

1

Mach number

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.gamma

1

Ratio of specific heats Heat capacity at constant pressure Mixing length limit

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.Cp

model.input.Cp

J/(kg*K)

nitf.l_mix_lim

0.05

m

nitf.lsubstar

nojac(min(min(nitf.C_m u*max(k, 0)^1.5/max(ep, sqrt(eps)), sqrt(2*max(k, 0))/(3*sqrt(max((ux (ux + vy)/3)^2 + 0.5*(uy + vx)^2 + (vy - (ux + vy)/3)^2 + (ux + vy)^2/9, eps)))), nitf.l_mix_lim)) nojac(max(nitf.rho*nitf.l substar*sqrt(max(k, 0)), 0.5*nitf.mu))

m

Limited mixing length

nitf.muT

Pa*s

Turbulent dynamic viscosity

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

31

Name nitf.nuT

Expression nitf.muT/nitf.rho

Unit m^2/s

Description Turbulent kinematic viscosity Turbulence help variable Turbulent kinetic energy source term

Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.gammaT

nojac(nitf.C_mu*nitf.rh o*max(k, 0)/nitf.muT) nojac(max(nitf.muT*(2* ux^2 + uy*(uy + vx) + vx*(uy + vx) + 2*vy^2 2*(ux + vy)^2/3), 0))

1/s

nitf.Pk

W/m^3

nitf.kinit

(100*subst(nitf.mu, T, m^2/s^2 300[K])/(subst(subst(nitf .rhoInt, nitf.pA, 1[atm]), T, 300[K])*nitf.l_mix_lim)) ^2 10*nitf.C_mu*(100*sub m^2/s^3 st(nitf.mu, T, 300[K])/(subst(subst(nitf .rhoInt, nitf.pA, 1[atm]), T, 300[K])*nitf.l_mix_lim)) ^3/nitf.l_mix_lim -1

Turbulent kinetic energy

nitf.epinit

Turbulent dissipation Domains 2, 5, rate 8, 11, 14, 17, 20, 23, 26, 29

nitf.hfPW

Full pressure work indicator Prandtl number

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.Pr

2*nitf.mu*nitf.Cp/(nitf.k 1 xxht + nitf.kyyht) nojac(1/(0.5882352941 176471 + 0.6507913734559685*n itf.Cp*nitf.muT/(nitf.kxx ht + nitf.kyyht) (0.6*nitf.Cp*nitf.muT/(n itf.kxxht + nitf.kyyht))^2*(1 exp(1.80775381515546 82*(nitf.kxxht + nitf.kyyht)/(nitf.Cp*nitf. muT))))) nitf.Cp*nitf.muT/nitf.Prt 1

nitf.Prt

Turbulent Prandtl number

nitf.kappaT

W/(m*K) 32

Turbulent thermal conductivity

Domains 2, 5, 8, 11, 14, 17,

Name

Expression

Unit

Description

Selection 20, 23, 26, 29

nitf.res_u

px + nitf.rho*u*ux + N/m^3 nitf.rho*v*uy - (d(2*ux 2*nitf.divu/3, x) + d(uy + vx, y))*(nitf.mu + nitf.muT) - nitf.Fx + 2*d(nitf.rho*max(k, 0), x)/3 nitf.rho*u*vx + py + nitf.rho*v*vy - (d(vx + uy, x) + d(2*vy 2*nitf.divu/3, y))*(nitf.mu + nitf.muT) - nitf.Fy + 2*d(nitf.rho*max(k, 0), y)/3 nitf.rho*nitf.divu + u*d(nitf.rho, x) + v*d(nitf.rho, y) 1.3^min(1 + niterCMP, 9) + if(niterCMP>=25, 9*1.3^min(25 + niterCMP, 9), 0) + if(niterCMP>=50, 90*1.3^min(50 + niterCMP, 9), 0) max(sqrt(emetric(u, v)*2^(2*gmg_level)), nitf.mu/(nitf.rho*(0.25* nitf.l_mix_lim)^2)) N/m^3

Equation residual

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.res_v

Equation residual

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.res_p

kg/(m^3*s)

Pressure equation residual Local CFL number

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

nitf.locCFL

1

nitf.time_step_inv

Hz

Inverse time step

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

Shape functions Name u Shape function Lagrange (Linear) Lagrange (Linear) Lagrange (Linear) Unit m/s Description Velocity field, x component Velocity field, y component Pressure Shape frame Material Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

v

m/s

Material

p

Pa

Material

33

Name k

Shape function Lagrange (Linear) Lagrange (Linear) Lagrange (Linear)

Unit m^2/s^2

Description Turbulent kinetic energy Turbulent dissipation rate Temperature

Shape frame Material

Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

ep

m^2/s^3

Material

T

K

Material

Weak expressions Weak expression (p - nitf.K_stress_tensorxx + 2*nitf.rho*max(k, 0)/3)*test(ux) nitf.K_stress_tensorxy*test(uy) nitf.K_stress_tensoryx*test(vx) + (p - nitf.K_stress_tensoryy + 2*nitf.rho*max(k, 0)/3)*test(vy) nitf.Fx*test(u) + nitf.Fy*test(v) - nitf.rho*(ux*u + uy*v)*test(u) nitf.rho*(vx*u + vy*v)*test(v) Integration frame Material Selection Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

Material

test(p)*(nitf.rho*nitf.divu - u*d(nitf.rho, x) - v*d(nitf.rho, y))

Material

-test(epx)*(nitf.mu + nitf.muT/nitf.sigmaeps)*epx test(epy)*(nitf.mu + nitf.muT/nitf.sigmaeps)*epy nitf.rho*(u*epx + v*epy)*test(ep) + nitf.gammaT*(nitf.Ceps1*nitf.Pk nitf.Ceps2*nitf.rho*ep)*test(ep) - 2*nitf.Ceps1*nitf.rho*(ux + vy)*ep*test(ep)/3 -test(kx)*(nitf.mu + nitf.muT/nitf.sigmak)*kx - test(ky)*(nitf.mu + nitf.muT/nitf.sigmak)*ky - nitf.rho*(u*kx + v*ky)*test(k) + (nitf.Pk - nitf.rho*nitf.gammaT*k)*test(k) - 2*nitf.rho*(ux + vy)*k*test(k)/3 -nitf.crosswindep - nitf.crosswindk

Material

Material

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23,

Material

nitf.streamlinek

Material

34

Weak expression

Integration frame

Selection 26, 29

nitf.streamlineep

Material

Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 Domains 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

-(nitf.k_effxx*Tx + nitf.k_effxy*Ty)*test(Tx) - (nitf.k_effyx*Tx + nitf.k_effyy*Ty)*test(Ty)

Material

-nitf.rho*nitf.Cp*(Tx*nitf.ux + Ty*nitf.uy)*test(T)

Material

nitf.crosswindns

Material

nitf.streamlinens

Material

-nitf.rho*nojac(nitf.time_step_inv/nitf.locCFL)*((u nojac(u))*test(u) + (v - nojac(v))*test(v))

Material

-if(d(nitf.rho, p)==0, 0.1*nitf.rho/1[atm], d(nitf.rho, p))*nojac(nitf.time_step_inv/nitf.locCFL)*(p - nojac(p))*test(p)

Material

-nitf.rho*nojac(nitf.time_step_inv/nitf.locCFL)*(k nojac(k))*test(k)

Material

-nitf.rho*nojac(nitf.time_step_inv/nitf.locCFL)*(ep nojac(ep))*test(ep)

Material

-nitf.C_eff*nojac(nitf.time_step_inv/nitf.locCFL)*(T nojac(T))*test(T)

Material

35

2.4.2

Thermal Insulation 1

Thermal Insulation 1 Selection

Geometric entity level Boundary Selection Equations Boundaries 131, 41, 5392

2.4.3

Wall 1

Wall 1

36

Selection

Geometric entity level Selection

Boundary Boundaries 9495, 9899, 102103, 106107, 110111, 114115, 118 119, 122123, 126127, 130131, 133152

Equations

SettingsSettings

Description

Value

Boundary condition Wall functions Variables Name nitf.ndflux Expression up(nitf.rho)*up(nitf.Cp)* nitf.C_mu^0.25*sqrt(ma x(k, eps))*if(down(try_catch( nitf.mu, 1))!= - 1, up(T) down(T), down(T) up(T))/nitf.Tplus Unit W/m^2 Description Normal conductive heat flux Selection Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152

nitf.meshVolInt

up(meshvol)

m^2

Volume of interior mesh element

37

Name nitf.unJump

Expression u*nojac(nitf.nxmesh) + v*nojac(nitf.nymesh)

Unit m/s

Description Jump in normal velocity

Selection Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152

nitf.KStressn_avx

nitf.K_stress_tensorxx*ni N/m^2 tf.nxmesh + nitf.K_stress_tensorxy*n itf.nymesh + nitf.K_stress_tensorxz*ni tf.nzmesh

Average viscous stress, x component

nitf.KStressn_avy

nitf.K_stress_tensoryx*n N/m^2 itf.nxmesh + nitf.K_stress_tensoryy*n itf.nymesh + nitf.K_stress_tensoryz*ni tf.nzmesh

Average viscous stress, y component

nitf.KStressn_avz

nitf.K_stress_tensorzx*ni N/m^2 tf.nxmesh + nitf.K_stress_tensorzy*ni tf.nymesh + nitf.K_stress_tensorzz*ni tf.nzmesh

Average viscous stress, z component

38

Name nitf.KStressTestn_av x

Expression nitf.K_stress_tensor_test xx*nitf.nxmesh + nitf.K_stress_tensor_test xy*nitf.nymesh + nitf.K_stress_tensor_test xz*nitf.nzmesh

Unit N/m^2

Description

Selection Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152

nitf.KStressTestn_av y

nitf.K_stress_tensor_test yx*nitf.nxmesh + nitf.K_stress_tensor_test yy*nitf.nymesh + nitf.K_stress_tensor_test yz*nitf.nzmesh

N/m^2

nitf.KStressTestn_av z

nitf.K_stress_tensor_test zx*nitf.nxmesh + nitf.K_stress_tensor_test zy*nitf.nymesh + nitf.K_stress_tensor_test zz*nitf.nzmesh

N/m^2

nitf.ujumpx

(u*nojac(nitf.nxmesh) + v*nojac(nitf.nymesh))*n ojac(nitf.nxmesh)

m/s

Velocity jump, x component

Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152

39

Name nitf.ujumpy

Expression (u*nojac(nitf.nxmesh) + v*nojac(nitf.nymesh))*n ojac(nitf.nymesh)

Unit m/s

Description Velocity jump, y component

Selection Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152 Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152

nitf.ujumpz

(u*nojac(nitf.nxmesh) + v*nojac(nitf.nymesh))*n ojac(nitf.nzmesh)

m/s

Velocity jump, z component

nitf.sigma_dg_ns

96*nojac(up(nitf.mu) + nitf.muT)*meshvol/nitf. meshVolInt

kg/(m^3*s)

nitf.rhoFace

up(nitf.rho)

kg/m^3

Density face value

Boundaries 9495, 98 99, 102103, 106107, 110111, 114115, 118119, 122123, 126127, 130131, 133152

40

Name nitf.umxTnFace

Expression (nitf.upwind_helpx*nitf. nxmesh + nitf.upwind_helpy*nitf.n ymesh + nitf.upwind_helpz*nitf.n zmesh