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

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

Nozzle Cascades for Turbines: Types and Design Features

The gas turbine is a rotary heat engine with double conversion of energy. In guide vanes (nozzles), the potential energy of steam is converted into kinetic energy, which is then converted into mechanical work by rotating the turbine shaft (rotor). The turbine rotor drives the rotor of the consumer machine, like in alternators, compressors, pumps, etc. [1]

Scheme of Turbine Flow Path
Figure 1 Scheme of turbine flow path [Huzel D.K., Huang D.H. Modern engineering for design of liquid-propellant rocket engines.- American institute of aeronautics and astronautics – 1992. ]
To increase the efficiency of turbine installations one must increase the thermal efficiency of the cycle, as well as the efficiency of individual elements of the installation’s thermal scheme. A familiar method of increasing the efficiency of the thermal cycle is by increasing the temperature of the working fluid in front of the turbine. However, this not only requires using high-temperature materials, but also requires cooling the blade apparatus. As a result, installation costs increase, and the efficiency of the turbine stages decreases [2]. Read More

Aircraft Engine Oil Supply Systems

It is no secret that one of the key issues in aircraft engine building is the choice of bearing units. Depending on the type, such units receive the radial load, hold the weight of the rotor, and face axial forces due to the action of the flow path and the secondary flow’s static pressures. Rolling bearings are commonly used in aircraft engines.

Ball Bearing
Figure 1 – Ball bearing –

To ensure their uninterrupted operation in hard conditions and different modes of friction with contacting parts, it is necessary to provide bearings with proper lubrication on the one hand, and adequate heat removal on the other. Heat generates because the power consumed to drive bearings is almost entirely converted into a heat flow. Furthermore, in aircraft gas turbine engines, hot engine parts–like the combustion chamber and turbine–also heat the bearings.

Oil Systems and Components.

In aircraft engines, a closed circulation lubrication system is widely used. One exception to this trend can be found in single-acting engines, where the system may be open and non-circulating. In such systems, fuel can be used as a lubricant. Read More

How AI Improves Axial Compressor Map Generation

A performance map is a key step in the design process of axial compressors. Performance maps represent the compressor characteristics and are used for compressor turbine matching and stall margin evaluation. Maps can also be used to compare different compressors, in order to determine which design would be most suitable for a given application. To accomplish these goals, maps usually plot the pressure ratio against corrected mass flow rate and corrected rotational speed. The map has a left bound limit called the surge line, and a right bound limit called the choke line.

Compressor Map
Figure 1: Compressor Map [1]
Now, how exactly do we generate these maps? The traditional approach is through physical experiments. The early prototype or finalized design is integrated into a test rig, which has components like pressure sensors, mass flow gauges, throttles, and others. Such a machine is then run at different operating points, which in turn allows for the plotting of pressure ratios. Unfortunately, this approach is highly time-consuming and requires expensive equipment. Moreover, if the operator over-throttles the mass flow rate, the compressor may pass its surge line. This can lead to an explosive discharge at the inlet, and thus to severe damage. Read More