Relative temperature effects

Discussion

In a system with rotating and stationary parts, the fluid temperature seen by a rotating surface differs from that seen by a stationary surface. To account for total temperature effects, you need to consider both the static and dynamic components:

Total Specific Enthalpy = Static Specific Enthalpy + Kinetic Energy

• is the static temperature.
• is the flow velocity.
  The definition depends on the reference frame:

  • Absolute:
  • Relative: , where ω is the rotation speed of the engine domain.

Several ​fluid temperature definitions are used in convection calculations:

• Static temperature, T_s is the temperature of a fluid that is not in motion. It is used to evaluate bulk fluid properties. Use the GetFluidTemperatureOfType plugin function to request solver temperature output if necessary.
• Total Absolute Temperature, T_{t, abs}, is the inlet fluid total temperature relative to a stationary component.
• Total Relative Temperature, T_{t, rel}, is the inlet fluid total temperature relative to a rotating component.

Modeling total temperature with Neglect Wall Rotation

The thermal solver calculates the total absolute fluid temperature, T_{t, abs}, as:

Where:

• is the static temperature, the temperature of a fluid that is not in motion.
• is the specific heat of the stream fluid material.
• is the fluid swirl velocity.
• is the fluid axial velocity.

The following example illustrates rotating fluid system showing swirl velocity, axial velocity, and wall velocity relative to a stator and rotating fluid flow.

In this case:

• The inlet temperature is interpreted as T_{t, abs}
• The fluid velocity is equal to 0, so T_s= T_{t, abs}.

Modeling total temperature effects on the wall due to rotating flow

The thermal solver computes the total relative fluid temperature, T_{t, rel}, seen by the rotating components, which is determined from the total enthalpy:

Where:

• is the fluid swirl velocity.
• is the fluid axial velocity, which is assumed to be 0.
• is the wall velocity, where ω is the rotor rotational rate and r is the radius. ​

The following example illustrates wall-rotation correction for a rotating disc, showing wall velocity, fluid swirl velocity, and angular rotation about the shaft axis.

The relationship between total temperatures is:

The thermal solver assumes the inlet fluid temperature is defined as T_{t, abs}.

Modeling total temperature effects on wall due to rotating flow

The thermal solve computes the total relative fluid temperature, T_{t, rel}, using:

The total absolute fluid temperature is then recovered from the total relative fluid temperature as:

The thermal solver assumes the inlet fluid temperature is defined as T_{t, rel}.

The thermal solver solves the heat transfer equations as a function of duct relative temperature, wall rotational speed, and swirl velocity in the specified relative reference frame.

The following example shows the relative reference frame (orange) between rotating and stationary parts.

You can define the angular velocity of this reference frame using the Relative Reference Frame type of the Rotation load. If you do not define the relative reference frame angular velocity, the thermal solver uses the maximum rotor rotational speed as the reference-frame angular velocity.

All 1D duct and stream elements in the 1D duct network reference the same relative reference frame for total temperatures when you set the Rotational Effects to Relative Temperature Reference Frame in defined thermal streams, and ducts coupling to the walls.

How to choose the relative temperature effects option

Scenario	BC temperature frame (what you specify)	Computed fluid temperature frame (what solver computes)	Results available in post-processing	Option to choose
No rotating wall effects are needed	Total absolute fluid temperature	Total absolute fluid temperature	Total absolute fluid temperature	Neglect Wall Rotation
Wall is rotating; swirl or rotation must be accounted for	Total absolute fluid temperature	Total absolute and total relative fluid temperatures	Total absolute and total relative fluid temperatures	Correct for Wall Rotation
User defines temperature in the rotating frame	Total relative fluid temperature	Total relative fluid temperature	Total relative and total absolute (converted) fluid temperatures	Relative Temperature Reference Frame

Accounting for rothalpy

When computing the total temperature effects in a relative reference frame, enable the Automatically Calculate Rothalpy option to conserve rothalpy, , the rotational stagnation enthalpy. ​When enabled, the thermal solver automatically accounts for windage and pumping due to rotation by adding the appropriate heat fluxes when computing the fluid total relative temperature. Under adiabatic conditions, rothalpy is conserved along the radius:

Where:

• is the angular velocity of the reference frame.
• is the fluid radius.

If this option is disabled, the following rotational kinetic energy term is not included:

Note:

Enable this option only if rotational heat effects are not already included through heat loads or boundary conditions; otherwise, disable it to avoid double counting.

Specifying swirl velocity

For all three total temperature effect methods, you can specify the swirl velocity or the swirl ratio. ​When you specify the swirl ratio, the solver computes the swirl velocity as:

Where:

• is the fluid swirl velocity.
• is the wall velocity.
• is the rotor rotational rate.
• is the radius.
• is the fluid swirl ratio, which is computed as:

Hands-on material

To gain experience with the topics discussed here, complete the following:

• Define convection boundary conditions using thermal streams and voids