Industrial Turbocharger

Turbocharger System Sample Model

A simple model of an industrial turbocharger has been developed to illustrate key concepts for modeling systems involving more than one turbomachinery component. These concepts include the calculation of net torque, the calculation of the shaft speed that balances torque, and shaft speed transients based on transient equations of motion (namely, T = I*dw/dt).

In the case of a turbocharger, a turbine provides the torque to drive a compressor. There is no gear box in this system, though representations of gearing, gear losses, bearing losses, etc. do not represent significant modeling challenges if the data (gear ratios, torque coefficients, etc.) is readily available. Similarly, starter motors and loads (e.g., generators) can be modeled as well.

The concepts and modeling methods developed are applicable to other systems involving multiple, linked turbomachines including:

  • Brayton cycles, including jet engines
  • Rankine cycles
  • liquid rocket turbopumps

System Description
The figure below represents the system schematic.

Air at ambient pressure and 20°C enters the compressor at point 1, and is discharged at point 2 (nominally 3.5:1 pressure ratio), the engine inlet. The nominal (design point) flow rate into the compressor is 10.47 kg/s, and the nominal shaft speed is 16000 rpm. The engine is modeled as a source of hot air (with combustion products neglected for simplicity), with a constant flow rate of 0.52 kg/s.

The engine representation is very simple: it adds 5.93MW of energy to the air. The nominal flow rate through the turbine, from point 3 to 4, is the sum of the flows through the compressor and engine: 10.99 kg/s.

The nominal exhaust pressure of the turbine is 1.9MPa. The exhaust system resistance (from turbine outlet to ambient) is estimated to be equivalent to a K-factor loss of about 16.8 at the dynamic head corresponding to the turbine exhaust. (This exhaust system resistance value will be varied parametrically later to test sensitivity).

The compressor is a centrifugal compressor, with an inlet meanline diameter of 230mm, a rotor outer diameter of 474mm, and a stator outer diameter of 676mm. The turbine is a radial design, with a stator inlet diameter of 709mm, rotor inlet diameter of 541mm, and a meanline outlet diameter of 252mm.

Basic Model Description
The model was developed using Thermal Desktop® and FloCAD®. The compressor was modeled using the performance map information (flow and efficiency versus pressure ratio). EZXY® plots of this information are provided below.

Performance Map Input for Compressor

Similarly, the performance of the turbine is plotted below. The basis for the turbine is total-static, which was defined as part of the TURBINE device information.

Solving for RPM at Zero Net Torque

In the above example, shaft speed is constant and the net torque is predicted. Often, the balance point is required: what shaft speed will result in equal but opposite compressor and turbine torques?

In SINDA/FLUINT, the Solver module can be used to find a traditional input (speed) given a traditional output (net torque), in a manner similar to the Excel goal seeking capability. The balance point was found to be about 16,050 RPM.

Shaft Speed Transient Example

To illustrate the solution of a combined mechanical and thermohydraulic set of equations, an artificial transient is run by perturbing the shaft speed from its equilibrium value (just above 16000 rpm) to 14000 rpm … the lowest value for which turbine and compressor data are available. Initially, this lower speed will cause a net positive value of torque. The shaft will then be allowed to speed back up to its design point.

A co-solved first-order ordinary differential equation (ODE) is set up to for the current shaft RPM, following the formula T = I*dw/dt (where T is the net torque, I is the rotational inertia, w is the rotor/shaft speed, and t is time).

An event duration of 360 seconds (6 minutes) proves enough for the shaft speed to return to its equilibrium value, as shown in the responses below:

Click here to fetch the Turbocharger Example from our User Forum

Advanced Pipes in FloCAD
Thursday November 14, 9-10am MT (8-9am PT, 11am-noon ET)
This webinar introduces advanced features for FloCAD pipes in addition to working with complex geometry. Complex geometry includes interior fins and surfaces for heat transfer, flow around enclosed objects, annular flow, concentric pipes, and more. FK Locators and TEEs as modeling objects will also be introduced.
Custom Heat Transfer and Pressure Drops
Tuesday November 19, 2-3pm MT (1-2pm PT, 4-5pm ET)
Do you know what the default assumptions are in FloCAD, and whether or not they apply in your situation? Do you know how far you can go past that starting point? The answer: pretty far. There are numerous mechanisms in FloCAD for adjusting factors, scaling uncertainties, and applying different or supplemental correlations. This webinar summarizes the options available to you to customize your flow models to make sure that they apply to each new situation you encounter.
Heat Exchangers: Detailed and System-level
Thursday November 21, 2-3pm MT (1-2pm PT, 4-5pm ET)
This is two webinars in one. The first explains the use and assumptions behind the FloCAD HX system-level modeling object. The second webinar describes detailed-level modeling of complex heat exchanger passages, including application of Compact Heat Exchanger (CHX) methods.
Starting in 2020, we will begin offering Introduction to Thermal Desktop and Introduction to RadCAD as either in-person training or online training, alternating between online and in-person every three months. The training uses lectures and demonstrations to introduce you to basic Thermal Desktop and RadCAD usage. Hands-on tutorials provide practice building models and interpreting results (tutorials are completed by students outside of the online class time).
The next training class will be an online format in January 2020:
  • Introduction to Thermal Desktop (and SINDA) - A three-part series on January 14, 16, and 21 from 9am to 12pm, Mountain time
  • Introduction to RadCAD - January 23 from 9am to 12pm, Mountain time
For up-to-date schedules, fees, and policies, visit our Product Training page. To register for the class above, complete our registration form and select "Online" for the Training Format.
If you are interested in product training for your company based on your schedule, please contact us to obtain a quote for training between 8-12 attendees. We can come to your facility or the lectures can be presented online. Descriptions of the available classes can be found in our course catalog.
To keep up with our training opportunities, take a look at our new Events and Training Calendar.