Scaling Laws in Turbomachinery Design and Operational Optimization

Turbomachines are undoubtedly complex. While designing them from scratch has the best potential to maximize performance, it is not always the best route.

With the help of similarity concepts and the associated nondimensional parameters, the preliminary design of a new machine can be based on features of an existing machine, even one which may have been designed for a different fluid, other flow conditions, or a different rotational speed.

Let’s say we have a turbomachine, in this case, a one-stage Centrifugal Compressor. It was designed for a specific mass flow rate and rotational speed value to achieve a certain pressure ratio at the best efficiency possible.

Table 1. Specification for Baseline Compressor
Table 1. Specification for Baseline Compressor
Figure 1. Baseline Centrifugal Compressor
Figure 1. Baseline Centrifugal Compressor

One would be able to get the same performance at any value of mass flow rate or rotational speed required just by scaling the machine (scaling is the process of changing a geometry while preserving similarity between the prototype and the model). And not just this specific point, but the whole performance map could be moved either to lower or higher mass flow rates. This is possible thanks to the concept of “Similarity”. Read More

SoftInWay Year End Review – 2022 Edition

In what feels like two shakes of a lamb’s tail, we’re wrapping up 2022! The year has been both challenging and rewarding, largely due to our incredible team, customers, and partners. So, what did SoftInWay get up to this year, and what is on the horizon for 2023?

New AxSTREAM Developments

Since the very first version of AxSTREAM, our development strategy has always been centered around the needs of our clients. After all, in an industry undergoing rapid technological advancements, it’s critical to have the tools and support needed to hit your project goals and keep up with the growing demand

2D view of pipe diffuser in AxSTREAM (left) & 3D view of pipe diffuser in AxSTREAM (right)
2D view of pipe diffuser in AxSTREAM (left) & 3D view of pipe diffuser in AxSTREAM (right)

Here is an overview of some key capabilities added inside the AxSTREAM platform, which include:

AxSTREAM for Turbines

  • Features expanded capabilities in incorporating both drilled and milled nozzles in turbine designs


AxSTREAM for Compressors

  • Is now capable of incorporating pipe diffusers into centrifugal compressor designs, enabling higher efficiency and performance in gas turbine engines


­AxSTREAM RotorDynamics & Bearing

  • Has several new features including but not limited to the:
    • Addition of finite element method for steady-state isothermal analysis of herringbone grooved gas journal bearings
    • Addition of finite element method for steady-state isothermal analysis of spiral grooved gas thrust bearings
    • Automated calculation of stiffness required to model the rigid connection between rotors
    • Ability to apply custom stress concentration factors during torsional harmonic analysis for both reciprocating and turbo machines.
AxSTREAM System Simulation

While the official launch of our newest product, AxSTREAM System Simulation, is set for next year, we showed off the beta version of this product in September during a webinar on environmental control systems (more on that later).

  • AxSTREAM System Simulation brings together legacy 0D and 1D solvers into a new and intuitive interface for a powerful solution. Through the integrated reduced-order modeling of dependent multidisciplinary systems, AxSTREAM System Simulation can eliminate the interface gap that exists between siloed software or sub-systems, thus speeding up development and reducing associated costs. More to come next year so stay tuned for the official release!
New Partnership with Ansys

In the summer of this year, we announced a technological partnership with Ansys to enable seamless integration between our AxSTREAM Platform and Ansys’ simulation software. The Ansys-SoftInWay partnership supports further digitization of a very streamlined workflow, from the initial design in AxSTREAM to analysis using Ansys’ 3D physics solvers Ansys® CFX®, Ansys® Fluent®, and Ansys® Mechanical™. The new workflow enables the integration of the high-fidelity simulations and optimization studies needed through Ansys Workbench to automate the entire development process in one continuous chain. Through this partnership, companies can fully automate the development process from the initial stages all the way to the completed design in one environment; a must-have for any engineering team developing turbomachinery and propulsion technology. Read More

Critical Speed Maps in Turbomachinery

For many years, one of the primary analysis techniques has been undamped critical speed analysis, and this technique is still performed today for the preliminary estimation of critical speeds and mode shape characteristics. First, let’s take a look at what this kind of analysis technique is and what it involves.

Critical speeds and their associated mode shapes are most influenced by the support (bearing and pedestal structure) stiffness magnitudes, the support locations, and the rotor’s mass and stiffness properties. Based on this, the following definition can be given. A critical speed map is a graph representing the effect of rotor support stiffness on the critical speed of the rotor. A general view of the critical speed map is shown in Figures 1-2.

Figure 1 Undamped Critical Speed Map [1]
Figure 2 Undamped Critical Speed Map in AxSTREAM RotorDynamics
Figure 2 Undamped Critical Speed Map in AxSTREAM RotorDynamics

With this definition in hand, the next question would be what is critical speed? Critical speed is the rotational speed that corresponds with a structure’s resonance frequency (or frequencies). A critical speed appears when the natural frequency is equal to the excitation frequency. The excitation may come from unbalance that is synchronous with the rotational velocity or from any asynchronous excitation. Read More

Choosing the Best Environmental Control System When Designing an Aircraft

As human beings, we are very vulnerable to environmental conditions, especially those in the stratosphere. Unlike cockroaches (which seem oddly equipped for pretty much anything), humans cannot survive in extremely low or extremely high ambient pressures or temperatures. Perhaps the best minds of our generation didn’t immediately think “how can I be more like this indestructible insect”, but nevertheless technological advancements have helped us get one step closer to their tenacity…at least in stratospheric conditions. Technology does not stand still though and is constantly improving and with it, we’re given more choices and variety in environmental control systems.

Figure 1 – Environmental Control System in an aircraft [2]
When designing environmental control systems (ECS), it is very important to understand that the top priority of these systems is to provide safety and comfort under absolutely any conditions, whether flying over the Sahara Desert or Alaska. We are talking about a minimum of 75 kPa and 20-24 °C. Relative humidity should range from 15 to 60% [1].

The ECS is usually split in one air conditioning machine (ACM) pack per engine. The ACM size is dictated by the ventilation requirement of 6 (g/s)/pax minimum (e.g. 1.2 kg/s minimum for the 200 pax capacity of A320; some 2 kg/s is the typical design value). This air can be taken both from the engine and through separate air intakes (but that’s a completely different story). Read More

Tip Clearance Loss Models in Centrifugal Compressors

This blog discusses tip clearance loss models in centrifugal compressor impellers with large relative clearances

In the flow path of turbomachines, there is a clearance between the tip of the rotor blades and the housing parts of the machine. This clearance is necessary in order to prevent the rotor from touching the stator during rotation of the impeller. The tip clearance value depends on the following features:

  • Deformation of the rotor under the action of gas, thermal and centrifugal loads
  • Housing deformations under the influence of air pressure and uneven heating
  • Clearance in bearings
  • Design features


There is a pressure gradient between the suction side and the pressure side, which results in a flow from one side of the blade to the other through the clearance. Studies of the flow in the tip clearance of the blades of turbomachines indicate its complex nature. The flow through the tip clearance affects the flow in the shroud section of the blade and has a significant impact on performance and efficiency. According to the results of the studies, an increase in the relative clearance by 1% reduces efficiency by 2%. Known methods for evaluating the effect of tip clearance on efficiency are most often reduced to a linear dependence of the reduction in efficiency on the relative clearance. This provides acceptable accuracy for engineering calculations with a relative clearance of no more than 3%.

The typical value of the tip clearance for the centrifugal compressor impeller is 0.2-0.5 mm. However, in some cases, the clearance is significantly higher and reaches 1-3 mm. An example would be the impellers of low-pressure compressors, which are made of plastic. Plastic is not a sufficiently rigid material, which requires the designer to significantly increase the tip clearance in order to avoid the impeller touching the housing part of the compressor in operation.

A feature of centrifugal compressors is the low blade height at the outlet of the impeller. Figure 1 shows the impeller of the compressor designed for pressure ratio ptr=2.4 with the diameter and height of the blades at the outlet, respectively, 220 mm and 15.1 mm. For such an impeller, with an absolute clearance of 0.5 mm, the relative clearance will be 3.3%. This means that simple clearance loss estimation methods will have a large margin of error for such an impeller. It should be taken into account that an impeller designed for the same outlet diameter, but at pressure ratio ptr=5, will have approximately half the blade height, respectively, and the relative clearance is twice as large.

Figure 1 - Scheme of a Centrifugal Compressor
Figure 1 – Scheme of a Centrifugal Compressor

Recently, there has been strong interest in small turbomachines. The impeller diameter of such compressors ranges between 50-70mm. The real estimation of clearance losses for this kind of compressor is a problem due to the large relative tip clearance. Read More

Stage Number Selection in Axial Aircraft Turbines

Choosing the number of stages during the development of axial turbines is one of the most controversial design tasks because it has many options to consider. This task does not have an exact solution, since it depends on the total turbine work, circumferential velocity and is determined by a combination of gas-dynamic, strength, construction, and technological factors. This blog will discuss some of the considerations for stage number selection of an axial turbine.

Using Stage Loading vs Parson’s Parameter

Designing turbines requires the use of complex parameters to simultaneously consider the influence of various factors on the characteristics of the turbine. Thus, the stage loading (mostly aircraft turbines) or the Parson’s parameter (stationary turbines and aircraft turbines) have been used for wide applications in turbines theory.

  • Stage loading is the ratio of the theoretical turbine work LU and the square of the circumferential velocity U.

­Stage loading Formula

  • Parson’s parameter y is the ratio of the circumferential speed to the speed equivalent to the isentropic heat drop.

­Parson's Parameter

High turbine efficiency is achieved, when these parameters are in the range μT = 1.2…1.6 (y=0.45…0.6), which can be seen in Figures 1 and 2 [1], respectively.

Figure 1 total to total turbine

Figure 2 Turbine Stage Hydraulic efficiency

Read More

An Introduction to Electric Motor Cooling Systems

Electric motors are all around us. They feature prominently in every major industry, and in many of the devices we use daily. For instance, this author’s personal morning routine relies on electric motors when using a coffee grinder, when turning on a desktop computer to read the news, and even when setting up an automatic cat feeder. Electric motors convert electrical energy into mechanical energy through interaction between the magnetic fields generated in the motor’s stator and rotor windings. To meet the power requirements of different industries and applications, electric motors are available in a variety of strengths and sizes.

Electric Motor
Figure 1. Electric Motor. SOURCE: [1]
Electric motors can have remarkably high efficiency ratings of over 90 percent. In other words, a large portion of the electrical energy that is supplied to the motor is successfully converted into mechanical output. The approximately 10 percent remaining is lost in the form of heat. Regardless of the application, one of the main challenges that motor designers face is that of thermal management.

Selection of the right electric motor is often based on a particular work or load requirement. When an electric motor is in operation and high performance is needed, the motor’s load can be increased (letting the motor draw more current), and greater heat is generated due to increases in rotor and stator losses. Since the heat flux in a system influences its thermal behavior, the motor’s temperature evolution depends on these losses. Read More

Fluid Swirl in Radial Channels of Turbomachines

Theoretical overview

In pumps, compressors, gas turbines, and powertrains with rotating parts, there are typically cavities between the spinning rotor and the fixed stator elements. The flow’s behavior at those cavities can significantly affect a machine’s temperatures, structural loads, vibrations, and overall efficiency. Similar radial cavities, where the flow is restricted between a rotating part and a non-rotating wall, are ubiquitous in the secondary flow channels of gas turbine engines (Figure 1).

Figure 1 – Example of secondary flows in a gas turbine engine [1]
Figure 1 – Example of secondary flows in a gas turbine engine [1]
Careful planning of secondary flows can be extremely useful. For example, since secondary flows influence the pressure in cavities, flows can be designed to compensate for axial loads acting on the rotor. Additionally, flow rotation in secondary flow channels critically impacts blade cooling design. For these reasons, a solid understanding of the processes occurring in radial channels is vital for high-quality design and optimization. Read More

Rotor Dynamics for Turbomachinery Engineers

A rotor is a body suspended through a set of cylindrical hinges or bearings that allow it to rotate freely about an axis fixed in space. It is the most critical component of any rotating machine; often operating at high speeds and within a wide speed range (Figure 1). Rotor dynamics is the branch of engineering that studies the lateral and torsional vibrations of rotating shafts. The main purpose of rotor dynamics is to predict the rotor vibrations and keep the vibration level under an acceptable limit. To meet stringent reliability requirements, each step of the rotor design should be based on an accurate rotor dynamics prediction.

Figure 1 The components of a rotating machine
Figure 1 The components of a rotating machine, [1]
A rotor dynamics analysis should accomplish several goals. It should predict critical speeds at which vibration due to rotor unbalance is severe and should be avoided. Relatedly, it should suggest modifications that would allow designers to increase a machine’s critical speeds. Rotor dynamics analysis should also predict natural frequencies of torsional vibration, as well as amplitudes of synchronous vibration caused by rotor unbalance. In addition, the analysis should predict dynamic instability (including oil whip), and suggest design modifications to suppress it. Lastly, the analysis should recommend balance correction masses and locations from measured vibration data. Read More

An Introduction to Pipe Diffusers in Centrifugal Compressors

A pipe diffuser is a special type of radial vane diffuser and is widely used in centrifugal compressors of gas turbine engines. Employing pipe diffusers can lead to increased efficiency in centrifugal compressors by an average of 2-4% compared to other vaned diffusers. The efficiency gains are especially prominent at high-pressure ratios (over 5.0), toward which we are seeing a growing trend in gas turbine engines.

Pipe Diffuser and assembly
Figure 1 (left): Single flow path of pipe diffuser & Figure 2 (right): Pipe diffuser assembly

Figure Source: Stanislaw Antas, Exhaust System for Radial and Axial-Centrifugal Compressor with Pipe Diffuser, Int J Turbo Jet Eng 2016;

Pipe Diffuser Geometry

The initial part of a pipe diffuser is a cylindrical section (throat), followed by the conical diffuser (Figure 3). The axis of the pipe diffuser must be tangent to the circle created by the tip of the centrifugal compressor, i.e., the circle defined by the impeller tip radius R2. The leading edge of the pipe diffuser channel is elliptical due to the oblique intersection of the cylindrical throat with the cylindrical surface of the diffuser radius R3. This intersection design results in gradually adapting the effluent flow from the impeller to the flow through the cylindrical and conical sections of the diffuser. The downstream duct of a compressor with a pipe diffuser is a diffusing trumpet, also called a “fishtail” diffuser. Read More