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

flow regimes

Introduction to Two-phase Flow

September 24, 2-3pm MDT

This webinar introduces basic concepts in two-phase flow modeling including quality, void fraction, flow regimes, slip flow, pressure drops and accelerations, and heat transfer.

No knowledge of CRTech software is required. However, references to the corresponding FloCAD features will be made to assist users of that product.

Click here to register

Introductory FloCAD Training

Class times: September 5, 10, and 12, 2019, 9:00 am to 12:00 pm MDT daily
Cost: no charge (attendees must have an active support contract)

CRTech will be hosting introductory training for FloCAD (Flow Modeling in Thermal Desktop). This is our standard FloCAD class previously hosted in a classroom environment and now restructured for an online teaching environment.

The class will introduce single-phase fluid modeling concepts and how to build fluid models within the FloCAD work environment. Topics covered include an introduction to fluid modeling components, geometric versus non-geometric modeling options, working with FloCAD Pipes, solution control, and an introduction to path and pipe libraries.

The class will be broken into three two- to three-hour sessions held over a 3 day period. The format will be online lecture and demonstration with opportunities to ask questions. Hands-on lab work will be provided to students to work on after each session. To gain the most from this class, students are encouraged to attend all three sessions.

Prerequisites: Attendees must have basic working knowledge of Thermal Desktop as many of its base features will not be covered in this class but their usage is required for FloCAD.

Eligibility Requirement: This class is a service to our customers. All attendees must have an active support contract. If you are unsure of your support status, please contact CRTech.

Click here to register