7.27. Heat Transfer Correlation Coefficient

This section is referenced in the following other sections

Simulation Setup: Correlation Heat Transfer Coefficient

7.27.1. Heat Transfer Correlation Coefficient

Scope: Aria Region
Summary: Specified heat transfer correlation coefficient model.
Description: Enables the user to specify a correlation model for use with computing heat transfer coefficients in conjunction with advective bar networks.

begin Heat Transfer Correlation Coefficient COEFF name

   Apply Gnielinski Film Gradient Correction [With Exponent {=} Exponent]

   Apply Hausen Entrance Effect Correction [Maximum Correction {=} MaxCorrection]

   Apply Wall Thermal Resistance = Scalar_String_Function F = string_function

   Characteristic Length {=} Dh

   Compute {annulus diameter ratio | characteristic length | density | fluid temperature | fluid velocity | friction factor | kinematic viscosity | prandtl number | reynolds number | wall prandtl number | wall temperature} [ Model {=} Value...  ]

   Density {=} rho

   Entrance Length {=} De

   Expansion Coefficient {=} beta

   Fluid Phase {=} {gas | liquid}

   Friction Factor {=} f

   Gravitational Constant {=} g

   Kinematic Viscosity {=} nu

   Laminar Correlation {=} Type {1 | 14 | 15 | 18 | 2 | 21 | 23 | 25 | 26 | 27 | 28 | 3 | 34 | 35 | 36 | 37 | 38 | 39 | 4 | 5 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 72 | 73 | 74}

   Laminar Correlation = Scalar_String_Function F = string_function

   Porosity {=} phi

   Prandtl Number {=} Pr

   Reynolds Number {=} Re

   Turbulent Correlation {=} Type {1 | 14 | 15 | 18 | 2 | 21 | 23 | 25 | 26 | 27 | 28 | 3 | 34 | 35 | 36 | 37 | 38 | 39 | 4 | 5 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 72 | 73 | 74}

   Turbulent Correlation = Scalar_String_Function F = string_function

   Temperature {=} t

   Transition Reynolds Number {=} Rex

   Velocity {=} v

   Wall Angle {=} theta

   Wall Length {=} l

   Wall Temperature {=} Tw

end Heat Transfer Correlation Coefficient COEFF name

7.27.1.1. Line Commands

Apply Gnielinski Film Gradient Correction

Syntax

Apply Gnielinski Film Gradient Correction [With Exponent {=} Exponent]

Summary

Enable a Gnielinski film temperature gradient correction factor to account for variation of fluid properties with temperature when computing the pipe and annular flow correlation heat transfer coefficients (Types 23, 25, 72-74).

Description

For gas phase convection the heat transfer coefficient correlations include a correction factor of the form $\left(\frac{T}{T_w}\right)^n$ .

For gas cooling $\left(\frac{T}{T_w}\right)>1.0$ $n=0$ .

For gas heating $0.5 \lt \left(\frac{T}{T_w}\right) \lt 1.0$ , $n$ varies for different gases but $n=0.45$ is generally recommended. For $CO_{2}$ and steam $n=0.15$ .

For liquids the correction factor is a function of bulk fluid and wall Prandtl number $\left(\frac{Pr_{b}}{Pr_{w}}\right)^{0.11}$ .

Parameter	Value	Default
{=}	{= \| are \| is}	–
Exponent	real	NONE

Apply Hausen Entrance Effect Correction

Syntax: Apply Hausen Entrance Effect Correction [Maximum Correction {=} MaxCorrection]
Summary: Enable the Hausen entrance effect correction factor for pipe and annular flow correlation heat transfer coefficients (Types 23, 25, 72-74).
Description: Applies a correction factor of the form $\left(1 + \frac{d_H}{L}^\frac{2}{3}\right)$ to the heat transfer coefficient where $d_H$ is the hydraulic diameter and $L$ is the distance from the pipe or annulus entrance to the point the flux is applied. By default the maximum value of the correction is 10, it can optionally be set using the MaxCorrection parameter in this command line. For $L \lt L_{min}$ the correction factor is not applied. This correction factor may only be applied when the correlation is being used with an advective bar model to represent the fluid flow.

Parameter	Value	Default
{=}	{= \| are \| is}	–
MaxCorrection	real	10

Apply Wall Thermal Resistance

Syntax: Apply Wall Thermal Resistance = Scalar_String_Function F = string_function
Summary: Model a thin wall using a wall thermal resistance specified as a scalar string function. The thermal resistance will be applied in series

Parameter	Value	Default
string_function	“string”	–

Characteristic Length

Syntax: Characteristic Length {=} Dh
Summary: Specifies the characteristic length for parameter computations such as Reynolds Number, etc.

Parameter	Value	Default
{=}	{= \| are \| is}	–
Dh	real	–

Compute

Syntax

Compute {annulus diameter ratio | characteristic length | density | fluid temperature | fluid velocity | friction factor | kinematic viscosity | prandtl number | reynolds number | wall prandtl number | wall temperature} [ Model {=} Value… ]

Summary

Specifies that model parameter be computed through such means as extraction, generic form, specific model, etc. Current options for the parameters and associated models include

CHARACTERISTIC LENGTH: {Hydraulic Diameter | Wetted Perimeter}

FLUID VELOCITY: This should always be set to the name of the advection velocity used in the energy equation. This will most likely be $\it{advection \ velocity}$ which is the internal variable used in Aria but may be set manually to anything else such as a user defined velocity field. FRICTION FACTOR: {Smooth Tube}

Parameter	Value	Default
ComputeCorrParam	{annulus diameter ratio \| characteristic length \| density \| fluid temperature \| fluid velocity \| friction factor \| kinematic viscosity \| prandtl number \| reynolds number \| wall prandtl number \| wall temperature}	–

Density

Syntax: Density {=} rho
Summary: Specify a density to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
rho	real	–

Entrance Length

Syntax: Entrance Length {=} De
Summary: Specify an entrance length for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
De	real	–

Expansion Coefficient

Syntax: Expansion Coefficient {=} beta
Summary: Specify an expansion coefficient by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
beta	real	–

Fluid Phase

Syntax: Fluid Phase {=} {gas | liquid}
Summary: Specify the fluid phase for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
FluidPhase	{gas \| liquid}	GAS

Friction Factor

Syntax: Friction Factor {=} f
Summary: Specify a friction factor to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
f	real	–

Gravitational Constant

Syntax: Gravitational Constant {=} g
Summary: Specify a gravitational constant by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
g	real	–

Kinematic Viscosity

Syntax: Kinematic Viscosity {=} nu
Summary: Specify a kinematic viscosity to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
nu	real	–

Laminar Correlation

Syntax: Laminar Correlation {=} Type {1 | 14 | 15 | 18 | 2 | 21 | 23 | 25 | 26 | 27 | 28 | 3 | 34 | 35 | 36 | 37 | 38 | 39 | 4 | 5 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 72 | 73 | 74}
Summary: Specifies the laminar correlation model.

Parameter	Value	Default
{=}	{= \| are \| is}	–
CorrelationType	{1 \| 14 \| 15 \| 18 \| 2 \| 21 \| 23 \| 25 \| 26 \| 27 \| 28 \| 3 \| 34 \| 35 \| 36 \| 37 \| 38 \| 39 \| 4 \| 5 \| 58 \| 59 \| 60 \| 61 \| 62 \| 63 \| 64 \| 65 \| 72 \| 73 \| 74}	–

Laminar Correlation

Syntax: Laminar Correlation = Scalar_String_Function F = string_function
Summary: Define Nusselt number using a scalar string function

Parameter	Value	Default
string_function	“string”	–

Porosity

Syntax: Porosity {=} phi
Summary: Specify a Porosity to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
phi	real	–

Prandtl Number

Syntax: Prandtl Number {=} Pr
Summary: Specify a Prandtl number to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
Pr	real	–

Reynolds Number

Syntax: Reynolds Number {=} Re
Summary: Specify a Reynold’s number to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
Re	real	–

Turbulent Correlation

Syntax: Turbulent Correlation {=} Type {1 | 14 | 15 | 18 | 2 | 21 | 23 | 25 | 26 | 27 | 28 | 3 | 34 | 35 | 36 | 37 | 38 | 39 | 4 | 5 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 72 | 73 | 74}
Summary: Specifies the turbulent correlation model.

Parameter	Value	Default
{=}	{= \| are \| is}	–
CorrelationType	{1 \| 14 \| 15 \| 18 \| 2 \| 21 \| 23 \| 25 \| 26 \| 27 \| 28 \| 3 \| 34 \| 35 \| 36 \| 37 \| 38 \| 39 \| 4 \| 5 \| 58 \| 59 \| 60 \| 61 \| 62 \| 63 \| 64 \| 65 \| 72 \| 73 \| 74}	–

Turbulent Correlation

Syntax: Turbulent Correlation = Scalar_String_Function F = string_function
Summary: Define Nusselt number using a scalar string function

Parameter	Value	Default
string_function	“string”	–

Temperature

Syntax: Temperature {=} t
Summary: Specify a Fluid Temperature to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
t	real	–

Transition Reynolds Number

Syntax: Transition Reynolds Number {=} Rex
Summary: Specify a transition Reynolds number to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
Rex	real	–

Velocity

Syntax: Velocity {=} v
Summary: Specify a velocity to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
v	real	–

Wall Angle

Syntax: Wall Angle {=} theta
Summary: Specify a wall angle by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
theta	real	–

Wall Length

Syntax: Wall Length {=} l
Summary: Specify a wall length by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
l	real	–

Wall Temperature

Syntax: Wall Temperature {=} Tw
Summary: Specify a Wall Temperature to either compute or specify by value for usage with a correlation convection coefficient.

Parameter	Value	Default
{=}	{= \| are \| is}	–
Tw	real	–

7.27.2. Use Correlation Convection Model

Syntax: Use Correlation Convection Model Name
Summary: Specifies correlation model for convection coefficient

Parameter	Value	Default
Name	string	–