New Series on Rotordynamics: Preface

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Welcome to our latest blog series on rotor dynamics! In this series we’ll be covering fundamentals and a general overview of the engineering discipline that is rotor dynamics, including some basic definitions, why it’s important, the different calculations, and the overall objectives and purposes for these calculations.

Axial Compressor Rotor

In the months ahead, you can expect to learn more about: Read More

Industrial Refrigerator Modeling

Refrigerators are an integral part of everyday life to the point where it is almost impossible to image our day without them. As in our everyday life, refrigeration units are also widely used for industrial purposes, not only as stationary units but also for transporting cold goods over long distances. In this blog, we will focus on the simulation and modeling of such an industrial refrigeration unit.

Picture 1 - Industrial Refrigerator
Industrial Refrigerator

Like any stationary refrigeration unit, a unit used for cooled transportation includes an intermediate heat exchanger, a pump, an evaporator, a compressor, a condenser, and a throttle. The most common refrigeration scheme uses three heat fluids in the industrial refrigeration cycle. There is Water, which is used for heat removal from Refrigerant- R134A and Propylene glycol 55%. These other fluids are used as intermediate fluids between the refrigerator chamber and refrigerant loop. The working principle of all fridge systems are based on the phase transition process that occurs during the refrigerator cycle shown in Figure 1. The propylene glycol is pumped into the evaporator from the heat exchanger, in which it cools and transfers heat to the refrigerant. In the evaporator, the refrigerant boils and gasifies during the heat transfer process and takes heat from the refrigerator. The gaseous refrigerant enters the condenser due to the compressor working, where its phase transition occurs to the liquid state and cycle repeats.
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Considerations when Designing Turbomachinery with sCO2 as a Working Fluid

Supercritical CO2 (sCO2) power cycles offer higher efficiency for power generation than conventional steam Rankine cycles and gas Brayton cycles over a wide range of applications, including waste heat recovery, concentrated solar power, nuclear, and fossil energy. sCO2 cycles operate at high pressures throughout the cycle, resulting in a working fluid with a higher density, which will lead to smaller equipment sizes, smaller carbon footprint, and therefore lower cost. However, the combinations of pressure, temperature, and density in sCO2 power cycles are outside the experience of many designers. Challenges in designing sCO2 cycles include turbomachinery aerodynamic and structural design, bearings, seals, thermal management and rotordynamics. According to the report from Sandia National Lab, compressors operating near critical point and turbines have received only TRL (technical readiness level) 4 and 5 out of 9. This blog discusses the impact on turbomachinery design.

Radial or Axial

The selection of radial or axial for turbomachinery is typically performed based on the operating conditions (adiabatic head H and inlet volumetric flow Q). Non-dimensional turbomachinery parameters of specific speed Ns and specific diameter Ds can be selected from NsDs charts to estimate size, speed, and type of turbomachinery. Turbomachinery types for a sCO2 recompression cycle with scales ranging from 100 kW to over 300 MW have been studied and concluded that systems below 10 MW will likely feature only radial turbines and compressors with a single-stage or low stage counts. Such recompression cycle can be simulated in AxCYCLE™ tool which is shown in Figure 1. As size increases, the most efficient configuration for the turbine and recompressor transitions from radial to axial at approximately 30 MW and 100 MW, respectively. Suitable types of turbomachinery and its components for different power range can be reviewed in Figure 2. A radial configuration for the main compressor was expected at all scales due to its lower volume flow and wider range to facilitate variation in gas properties due to operation near the critical point.

Recompression Cycle simulated in AxCYCLE
Figure 1 – Recompression Cycle Simulated in AxCYCLE

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When to Upgrade Your Pump

[:en]The typical life cycle cost of an industrial pump depends on its maintenance and energy consumption. Hence, it is necessary to keep track of the pump performance and do periodic maintenance to achieve performance level close to the performance predicted by the manufacturer. There are many instances in which maintenance becomes very costly to achieve the required performance. This is the point when owners must decide about whether to upgrading the system. Figure 1 shows the life cycle cost of typical industrial pumps.

Figure 1 Life Cycle Cost of Typical Industrial Pump
Figure 1 Life Cycle Cost of Typical Industrial Pump

In recent years, there have been many innovations in implementing newer materials as well as improvements in hydraulics. Improving pump designs is an ongoing process with designers looking for increasing performance by a few percentage points. The goal of the present pump manufacturers is to offer higher efficiency and reliability, but replacing an older pumps with newer pumps can mean higher costs. The focus for replacing the internals of the pumps with improved design has gained prominence since many of the components, like the casing and rotor, of the existing pumps can be reused. So instead of replacing the entire pump, it can be upgraded or retrofitted. When it comes to an upgrade, the first thing that should be considered is the return on investment which includes the initial investment, operating costs, and the reduction in energy consumption due to the improved pump performance.

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Introduction to Heat Recovery Steam Generated (HRSG) Technology

[:en]The acronym HRSG (Heat Recovery Steam Generated) is in different sources describing the operation of cogeneration and heating plants, but what does it mean? Heat Recovery Steam Generated (HRSG) technology is a recycling steam generator which uses the heat of exhaust from a gas turbine to generate steam for a steam turbine generating electricity.

The simplest scheme of a Combined Cycle Gas Turbine (CCGT) is presented in Figure 1.

The simplest scheme of CCGT
Figure 1: The simplest scheme of CCGT.

In Figure 1, the exhaust flue gases temperature on the outlet of the turbine is equal to 551.709 ℃. This is a too high a temperature to release the gasses into the environment. The excess heat is able to be disposed of while receiving additional electric power which is approximately equivalent to 30% of the capacity of a gas turbine.

To reach the maximum economical and eco-friendly criteria possible for the installation, many pieces of equipment are used including: a waste heat boiler (HRSG); turbines with a selection for a deaerator (Turbine With Extraction, Deaerator); feed and condensate pumps (PUMP2, PUMP); a condenser (Condenser); and a generator (Generator 2). Exhaust gases entering into the HRSG transfer heat to water which is supplied by the condensate pump from the steam turbine condenser to the deaerator and further by the feed pump to the HRSG. Here boiling of water and overheating of the steam occurs. Moving further, the steam enters the turbine where it performs useful work.

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7.2 Optimal Design of the Axial Turbines Flow Paths Taking into Consideration the Mode of Operation

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For demonstration of opportunities of the developed complex of the methods, algorithms and mathematical models for solving the problems of optimal design of the turbine units taking into account their mode of operation [38, 40–42] the results of optimization research of turbine expander flow path and of gas turbine unit GTU GT-750-6M low pressure turbine flow path are presented below.

7.2.1 Optimization of Rendering Turbine Expander Unit (RTEU) Flow Path of 4 MW Capacity With Rotary Nozzle Blades

In gas pipelines, natural gas is transported under the pressure 35–75 atmospheres. Before serving the natural gas to the consumer its pressure must be lowered to the level of pressures local supply systems. At the moment gas distribution stations widely are using technologies of utilization of natural gas let-down pressure before serving the consumer. To extract energy from compressed gas the special rendering turbine expander units (RTEU) are used in which the potential overpressure energy is converted into mechanical work of a rotor rotation of a turbine, which serves as generator drive.

Seasonal unevenness of natural gas consumption, usually caused by environmental temperature, leads to a deeply no projected RTEU operation modes and adversely affect their performance and service life. For example, the gas flow through the flow path of the RTEU during the year may vary in ranges from 0.25–0.35 to 1.05–1.25 from the rated value. The foregoing attests to the relevance and necessity of taking into account the factor variability of operation loads during the selection of the basic geometric parameters of the RTEU FP.

This section provides results of optimization of 4-stage flow path of existing design of RTEU taking into account real operation modes of it, using the developed algorithm [40].

Operating conditions of the considered RTEU are characterized by significant monthly uneven mass flow rate of the working fluid through the flow path of the unit with fixed heat drop and rotor speeds:


The mass flow rate of natural gas, depending on the operating mode, changed in the range from 4.94 to 20.66 kg/s (the mass flow rate at the design mode is Gnom = 16.66 kg/s).

At present several ways to regulate the mass flow through the RTEU FP are known. The changing of the walk-through sections of nozzle cascade (NC), thanks to the use of rotary nozzle blades, is the most effective.

It is known that the implementation of the rotary nozzle blades can significantly extend the range of workloads of the turbine installation and improve performance indicators of FP. However, to get the maximum effect from the rotation of the nozzle blades, there is a need to further address the challenge of defining optimal angles α1e for each stage, depending on the
operating mode of the RTEU FP. Read More

7.1 Multi-Criterion Optimization of HPC of Powerful Steam Turbines at Nominal Operational Mode

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Chapter 7 Introduction: Experience and Examples of Optimization of Axial Turbines Flow Paths

In this chapter, as an example of practical use of the developed theory of optimal design of axial turbines flow paths, the results of the studies, related to the optimization of parameters of flow path of the high pressure cylinders (HPC) of 220, 330 and 540 MW capacities turbines, operating at nominal mode, as well as examples of optimization turbo-expander and low pressure turbine of gas turbine unit, taking into account the mode of its operation, are presented. The entire complex of calculation research was conducted using mathematical models of flow path (FP) of axial turbines, described in Chapter 2.

In addition, in the studies variants of mathematical models of FP “with the specified profiles” [38] were also used, which allowed with more accuracy determine geometric characteristics of turbine cascades, in particular, the inlet geometric angles of working and nozzle cascades, that are changing with the changing of stagger angles of the profiles. The latter had a significant impact on the amount of additional losses related to the incidence angle of inlet flow of working fluid. Read More

6.7 Optimization with the Mass Flow Rate Preservation Through the Cascade

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Review of research on the application of the complex tangential lean and its optimization, as well as conducted computational research has shown that using of complex lean gives the possibility to increase aerodynamic efficiency of turbine cascades. However, as previously noted, research on optimization of complex tangential lean with preserving mass flow rate through the cascade with high precision, currently we do not have. Using developed optimization approach it is possible to preserve in optimal cascade mass flow rate at the level of the initial cascade with a high accuracy.

Complex tangential lean reduces integral losses by reducing secondary losses. It is known, that with increasing  l/b there is a reducing in the part of the secondary losses in integral losses and, accordingly, the benefit from optimization has to diminish.

Relative height criterion was taken not  l/b, but the cascade’s characteristic relation a/l, by analogy with the flows in the swivel tubes of rectangular cross-section.

Optimization problem is solved using two methods of stacking line parameterization. Research of the efficiency of the algorithm consists in attempts of optimization of turbine cascade at different a/l = 0,16; 0,23; 044 by changing of the blade height. It should be noted that for the blades with a/l ≤ 0.16 optimization, using both methods of stacking parameterization, no longer led tot he reducing losses compared to the cascade without lean.

The size of the throat varies slightly due to the changing of stagger angle of the profile, which is associated with the preserving of the mass flow rate.

Special attention was given to the FMM accuracy, since it determines the validity of the results obtained with used optimization approach. Criterion of the accuracy is deviation of the values of the target function and the constraint function, which we obtain in FMM and in checking CFD calculation.

6.7.1 Optimization with Various a/l Using Method 1

The results of the optimization for a/l = 0.44

Taking into account the experience of previous studies, in Table 6.3 the ranges of parameters variation have shown. The correctness of their choice is confirmed by the fact that the optimal combination of varied parameters falls in this range already at the first step of the optimization.

Table 6.3 Ranges of variation of parameters optimization
Table 6.3 Ranges of variation of parameters optimization

Then, a plan is created in accordance with the algorithm and relevant CFD calculations are produced (Table 6.4). The objective function – integral losses ζ, restriction function – mass flow rate through the calculation channel G Read More

6.6 The Influence of Complex Tangential Lean on the Flow in Circumferential Turbine Cascade

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Object of study and boundary conditions are identical to the turbine cascade, that described in the previous section, with the exception of the relative height of the blade, which in this case amounted to l/b = 0.714. Complex lean was carried out according to 2-nd method without changing the stagger angle of the profile.

Using proposed algorithm (section 6.4) the optimal blade’s shape of the specified turbine guide blade was found on the sixth step of the variation parameters range refinement.

All 56 configurations of turbine blades shape were counted.

To solve the same problem using genetic algorithm, probably, hundreds of calculations would have required. The Table 6.1 shows the best value of the varied parameters and the best value of target function for each of the optimization stages.

At the 1–5 stages optimization of minimum objective function fall on the border range of variation parameters, at that on 4-th phase the function is minimal on the right edge of the border of variation parameters range, while on 5-th phase the function is minimal on the left edge. As a result, after the 6-th phase the values of the optimal parameters became Ys = 0.77 and Yh = 0.80.

Table 6.1 History of optimization studies
Table 6.1 History of optimization studies

Fig. 6.14 shows isolines of the objective function in the space of parameters Ys and Yh. 

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Turbomachinery and Rockets – a Historical/Technical Evolution


Quite surprisingly, rockets in their primal form were invented before turbomachinery, even though turbines and pumps are both present in modern launcher engines. However, it is interesting to note that  both can be traced to the same ancestor. In this post we will discuss some of the history and technical evolution of rockets and turbomachinery – and this all starts with an old pigeon.

Figure 1. Steam Turbine and Rocket


Circa 400BCE, a Greek philosopher and mathematician named Archytas designed a pigeon-like shape made out of wood that was suspended with wires and propelled along these guides using steam demonstrating the action-reaction principle long before Newton formalized it as a rule in Physics. As we know today, the faster and the more steam escapes the pigeon, the faster it goes. Turn this 90 degrees to have the bird face upward, and you have a very basic rocket concept. However, rockets are a lot more complex than this, and do not typically use steam (except in the case of liquid hydrogen + liquid oxygen propellants) as the propelling fluid.  Read More