Test Case 1 :Test Case 1 :Mixed convection in vertically flowing heated pipeMixed convection in vertically flowing heated pipe

(buoyancy aiding or opposing)(buoyancy aiding or opposing)

Problem specifications:

Re=2650

Pr=0.71

Wall constant heat flux

Boussinesq approximation

Heat transfer Regimes:

Gr/Re2=0.000 Forced Convection

Gr/Re2=0.063 Forced/Mixed Convection

Gr/Re2=0.087 Re-Laminarization

Gr/Re2=0.241 Recovery

KNOO CFD @ Manchester: Heat transfer test cases

AGR working schemeAGR working scheme

Relevance to AGR and VHTR

V gradient away from wall=> Turbulence increase

V gradient nearer wall=> Turbulence decrease

buoyancy aidingbuoyancy aiding

buoyancy opposingbuoyancy opposing

Buoyancy aiding or opposing vertical pipe flowBuoyancy aiding or opposing vertical pipe flow

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.01 0.1 1 10Bo

Nu/Nu

0

Launder & Sharma Model

Cotton & Ismael Model Suga ModelData of Carr et al (1973)DNS of You et al (2003)

Data of Easby (1978)Data of Parlatan et al (1996)

)/( .. 8042534 rPeRGr108Bo ×=

Nu/Nu0 against ‘buoyancy parameter’, [Hall and Jackson ]

0.3

0.5

0.7

0.9

1.1

1.3

1.5

0.01 0.1 1 10Bo

Nu/Nu

0

Launder & Sharma Model (CONVERT)

Large Eddy Simulation (STAR-CD)

Data of Steiner (1971)

Data of Carr et al (1973)

Data of Parlatan et al (1996)

DNS - You et al (2003)

STAR-CD Quasi DNS [Y. Addad ]

" " 1. 6.3 18.

. 0.2 8.8 10.5.

STAR quasi DNS r R z

You et al DNS r R z

φ

φ

+ + +

+ + +

Δ = Δ = Δ =

Δ = Δ = Δ =

)/( .. 8042534 rPeRGr108Bo ×=

0.3

0.5

0.7

0.9

1.1

1.3

1.5

0.01 0.1 1 10Bo

Nu/Nu

0

Launder & Sharma Model (CONVERT)

Suga Non-Linear Eddy Viscosity Model (CONVERT)

k-omega-SST Model (STAR-CD)

k-omega-SST Model (Code_Saturne)

Large Eddy Simulation (STAR-CD)

DNS - You et al (2003)

K-omega not sensitive to buoyancy effect

0.3

0.5

0.7

0.9

1.1

1.3

1.5

0.01 0.1 1 10Bo

Nu/Nu

0

Launder & Sharma Model (CONVERT)

k-omega-SST Model (STAR-CD)

Lien & Durbin v2f Model (STAR-CD)

Manchester v2f Model (Code_Saturne)

Large Eddy Simulation (STAR-CD)

DNS - You et al (2003)

Good predictions by V2F models

0.3

0.5

0.7

0.9

1.1

1.3

1.5

0.01 0.1 1 10

Bo

Nu/Nu

0

Launder & Sharma Model (CONVERT)Cotton & Ismael Model (CONVERT)Suga Non-Linear Eddy Viscosity Model (CONVERT)Lien-Chen-Leschziner k-eps Model (STAR-CD)k-omega-SST Model (STAR-CD)Lien & Durbin v2f Model (STAR-CD)k-omega-SST Model (Code_Saturne)Manchester v2f Model (Code_Saturne)Large Eddy Simulation (STAR-CD)DNS - You et al (2003)

“standard” STAR k-epsilon model (Lien Chen Leschziner)

5

10

15

20

25

DNS of You et

al (2003)Launder &Sharma

(CONVERT)

Cotton & Ismael(CONVERT)Suga NLEVM(CONVERT)Standard k-

epsilon (STAR-

CD)

Lien & Durbinv2f (STAR-CD)Manchester v2f(Code_Saturne)k-omega-SST

(STAR-CD)k-omega-SST

(Code_Saturne)

Large EddySimulation

Cf x 1000 - Nu

Nusselt number

Friction coefficient

Results for Fully-Developed Forced Convection. (no buoyancy)

Expt. of Polyakov & Shindin

Buoyancy aided heated pipe flow

Gr/Re**2 = 0.000Gr/Re**2 = 0.000

Buoyancy aided heated pipe flow

Gr/Re**2 = 0.087 (relaminarization)Gr/Re**2 = 0.087 (relaminarization)

Buoyancy aided heated pipe flow

Gr/Re**2 = 0.087 (relaminarization)Gr/Re**2 = 0.087 (relaminarization)

Buoyancy aided heated pipe flow

Gr/Re**2 = 0.087 (relaminarization)Gr/Re**2 = 0.087 (relaminarization)

Buoyancy aided heated pipe flow

Gr/Re**2 = 0.241 (recovery)Gr/Re**2 = 0.241 (recovery)