# Blunt Body

- Type
- Body in Crossflow Nu
- Subtype
- Body in Crossflow

Index | UI Name (.flo label) | Description |
---|---|---|

1 | Shape (SHAPE_ID) |
Shape of the body in the cross flow. The shapes available in the correlation are mentioned in the Formulation section. |

2 | Velocity Input Type (VEL_ID) |
Methods available for the user for velocity input:- Chamber
- User Input
- RPM based
Further discussions are in the Formulation section. |

3 | Velocity (FLOW_VEL) |
This is activated only if User Input is selected as the “Velocity Input Type”. It takes the user input velocity. |

4 | Characteristic Length (CHAR_LEN) |
The characteristic length/diameter of the fluid flow. “d” in the Formulation section. |

5 | Outer Radius (OUTER_R) |
The stator outer radius. This is activated only if
RPM Based is selected as the
“Velocity Input Type”. If “Auto”, then Outer Radius = 0.5 * Characteristic Length. |

6 | Tip Speed Ratio (TIP_SPD_RATIO) |
The frame tip speed ratio, user-defined. |

7 | HTC Multiplier (HTC_MULT) |
A constant multiplier to scale the value of heat transfer coefficient obtained from the correlation. |

## Formulation

This correlation uses a Nusselt number that can be found in references 1, 2, and 3. A linear interpolation is used if the Re is in the transitional regime.

Reynolds Number:

With:

${V}_{ext}$ : The external fluid velocity.

$d$ : The characteristic length/diameter of the fluid flow.

${\mu}_{T}$ : The external fluid flow viscosity, at the film temperature.

$\rho $ : The external fluid density.

Velocity Input Type | Comments | Formulation |
---|---|---|

Chamber | This is the default method. This takes the velocity that is calculated in the fluid chamber attached to the convector. | |

User Input | In this method, you can directly input the velocity. | |

RPM Based | This method requires the outer radius and tip speed ratio for calculation of the velocity. It is further explored in Formulation section. |
${V}_{ext}=\frac{\omega *OR}{TipSpeedRatio}$
With: $\omega $ : The angular speed of the rotor. $OR$ : The outer radius. $TipSpeedRatio$ : The user-defined tip speed ratio. |

Nusselt’s number:

Shape Name in GUI | Shape Demonstration | Re | C | m |
---|---|---|---|---|

Square | 2.5*10^{3 }– 8*10^{3} |
0.180 | 0.699 | |

5*10^{3} - 10^{5} |
0.102 | 0.675 | ||

Rhombus | 5*10^{3} - 10^{5} |
0.25 | 0.588 | |

Horizontal Ellipse | 2.5*10^{3 }– 1.5*10^{4} |
0.25 | 0.612 | |

Vertical Ellipse | 3*10^{3 }– 1.5*10^{4} |
0.096 | 0.804 | |

Horizontal Hexagon | 5*10^{3} - 10^{5} |
0.156 | 0.638 | |

Vertical Hexagon | 5*10^{3 }– 1.95*10^{4} |
0.162 | 0.638 | |

1.95*10^{4} - 10^{5} |
0.0395 | 0.782 | ||

Thick Vertical Plate | 3*10^{3 }– 2*10^{4} |
0.264 | 0.66 | |

Thin Vertical Plate | 4*10^{3 }– 1.5*10^{4} |
0.232 | 0.731 | |

Horizontal Triangle | 3*10^{3 }– 2*10^{4} |
0.246 | 0.61 | |

Cylinder | This follows Churchill-Bernstein convection correlation. For more information, see Heat Transfer Coefficients (HTC) Correlations and view the section Churchill-Bernstein (Cylinder in Cross Flow). |

Index | .flo label | Description |
---|---|---|

1 | TNET | Thermal network ID which has the convector where this correlation is used. |

2 | CONV_ID | Convector ID which is using this correlation. |

3 | SHAPE | Shape of the body in cross flow. |

4 | CHAR_LEN | Characteristic length. |

5 | OUTER_R | Only appears if RPM Based velocity type is selected. Displays the value of outer radius used in the calculations. |

6 | TIP_SPD_RATIO | Only appears if RPM Based velocity type is selected. Displays the value of tip speed ratio used in the calculations. |

7 | VELOCITY | The velocity used in the calculations. |

8 | PR | Prandtl number. |

9 | RE | Reynolds number. |

10 | NU | Calculated Nusselt number. |

11 | HTC | Calculated heat transfer coefficient. |

## Heat Transfer Correlation References

- Petit J.P., Transfert de chaleur et de masse, Cours de l’Ecole Centrale de Paris.
- Incropera, F. and Dewitt, D. Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2006.
- Jakob, M., Heat Transfer, Vol. 1, Wiley, New York, 1949.