VVT30 - Rotational effects for non-co-rotating structures

Description

This validation case examines the rotational effect for non-co-rotating structures modeling convective heat transfer between the rotor and the stator with three different methods using:

Case A: The duct's elements are coupled to the walls with the Convection Coupling type of the Thermal Coupling - Convection simulation object.

Case B: The duct's nodes are coupled to the walls with the Duct Node Convection Coupling type of the Thermal Coupling - Convection simulation object.

Case C: A Thermal Stream load.

Geometry

The axisymmetric modeling technique is used to model non-co-rotating structures. Six plates are sketched on the XZ plane with a length of 18 in and a width of 2 in.

Simulation model

This model uses the Simcenter 3D Multiphysics solver.

A 2D mesh is generated using axisymmetric linear quadrilateral elements that are 1 in in size for rotor (green) and stator (blue). The 1D elements are axisymmetric ducts with a mass flow.

The meshed elements have the following material and physical properties:

• Shell material for plates: Steel
  • Mass density: ρ = 7829 kg/m³
• Environmental fluid material : Air
  • Mass density: ρ = 1.2041 kg/m³
  • Specific heat at constant temperature: C_p = 1004.5 J/kg·K

The following boundary conditions are applied :

In all three cases:

• Duct Fan/Pump type of the Duct Flow Boundary Conditions simulation object with the mass flow of1 lbm/s.
• Model Subset ZX type of the Rotation load on the rotors in blue with the angular velocity w =2 000 rad/s along the z-axis of rotation.
• Relative Temperature Reference Frame type of the Rotation load to define the reference frame for inlet temperatures with the defined angular velocity equal to half the rotor's angular velocity, i.e. Ω = 1000 rad/s around the z-axis.

In Case A:

• Convection Coupling type of the Thermal Coupling - Convection simulation object on the inner edge of the rotor with the heat transfer coefficient equal to 1e-8 Btu/(hr·ft²·ºF). The rotational effects option is set to Relative Temperature Reference Framewith the swirl velocity equal to 825 ft/s.
• Temperature constraint on the duct inlet is 500 ºF.

In Case B:

• Duct Node Convection Coupling type of the Thermal Coupling - Convection simulation object on ducts nodes coupled to the inner edge of the rotor with the heat transfer coefficient equal to 1e-8 Btu/(hr·ft²·ºF).
• Two-Sided Rotational Total Temperature Effect type of theDuct Flow Boundary Conditions simulation object. The rotational effects option is set to Relative Temperature Reference Frame with the swirl velocity equal to 825 ft/s. The swirl input type for Side B same as Side A.
• Temperature constraint on the duct inlet is 500 ºF.

In Case C:

• Two-Sided Stream on Edges type of Thermal Stream load with the inlet temperature of 500 ºF. The rotational effects option is set to Relative Temperature Reference Frame with the swirl velocity equal to 825 ft/s with the heat transfer coefficient equal to 1e-8 Btu/(hr·ft²·ºF). The swirl input type for Side B same as for the Side A.

The default solver parameters are selected.

The following solution options are set:

• Solution Control: Element Discretization is set to Finite Element Method in the Thermal Solution Parameters modeling object.

• Total Temperature is selected as a requested thermal results option.

Theory

To consider the rothalpy conservation in the relative frame of reference for the rotor-stator cavity, the following equation is used to compute the fluid total relative temperature along the radius:

where:

• C_p is the fluid specific heat.
• T_rel is the total temperature of fluid relative to a rotating component.
• Ω is the specified angular velocity of the reference frame.

The total absolute and relative temperatures with the constant specific heat are defined using the following equations:

where:

• V_ϕ is the absolute tangential fluid velocity.
• T_abs is the total absolute fluid temperature.
• T_s is the static fluid temperature.
• r is the fluid radius.

The relationship between absolute and relative fluid temperatures is:

where Ω is the specified angular velocity of the reference frame.

Since static temperatures are equal for the fluid and walls, this leads to:

The fluid's total absolute temperature can be written based on its total relative temperature:

An equation for T_rel,wall was used to calculate theoretical values for the total relative temperature of the rotor, T_rel,rotor, and the stator, T_rel,stator.

A relationship between the total absolute and relative temperature can be defined for the walls:

where Ω_w is the specified angular velocity of the wall.

An equation for T_abs,wall is used to calculate theoretical values for the total absolute temperature of the rotor, T_abs,rotor, and the stator, T_abs,stator. Because the stator's angular velocity is 0 rad/s, therefore, the total absolute and total relative temperatures are equal.

Results

The following table compares the total relative temperature for the stator and the rotor walls, and the relative temperature of fluid that is calculated by the thermal solver with the analytical solution. The results for all three cases are in good agreement with theoretical values. Case C that models the heat transfer using thermal streams provides better accuracy compared to Case A and B that model heat transfer using thermal couplings of ducts to the walls.

The following table compares the total absolute temperature for the stator and the rotor that is calculated by the thermal solver with the analytical solution. The results for all three cases are in good agreement with theoretical values. Case C that models the heat transfer using thermal streams provides better accuracy compared to Case A and B that model heat transfer using thermal couplings of ducts to the walls.