Heat Recovery Steam Generator Design

Heat recovery steam generators (HRSGs) are used in power generation to recover heat from hot flue gases (500-600 °C), usually originating from a gas turbine or diesel engine. The HRSG consists of the same heat transfer surfaces as other boilers, except for the furnace. Since no fuel is combusted in a HRSG, the HRSG have convention based evaporator surfaces, where water evaporates into steam. A HRSG can have a horizontal or vertical layout, depending on the available space. When designing a HRSG, the following issues should be considered:

hrsg-boiler
Figure 1: Schematic of a HRSG boiler
  • The pinch-point of the evaporator and the approach temperature of the economizer
  • The pressure drop of the flue gas side of the boiler
  • Optimization of the heating surfaces

The pinch-point (the smallest temperature difference between the two streams in a system of heat exchangers) is found in the evaporator, and is usually 6-10 °C, which can be seen in Figure 2. To maximize the steam power of the boiler, the pinch-point must be chosen as small as possible. The approach temperature is the temperature difference of the input temperature in the evaporator and the output of the economizer. This is often 0-5 °C. The pressure

hrsg-boiler-2
Figure 2: Example of a heat load graph for HRSG boiler

drop (usually 25-40 mbar) of the flue gas side also has an effect on the efficiency of power plant. The heat transfer of the HRSG is primarily convective. The flow velocity of the flue gas has an influence on the heat transfer coefficient. The evaporator of heat recovery boiler can be of natural or forced circulation type. The heat exchanger type of the evaporator can be any of parallel-flow, counter-flow or cross-flow. In parallel-flow arrangement the hot and cold fluids move in the same direction and in counter-flow heat exchanger fluids move in opposite direction.

 

The Significance of Quantifying Uncertainties in Turbomachinery CFD

The increased use of CFD for turbomachinery design is an outcome of the increasing accuracy thanks to high computational resources. Although the benefits of such computations are strong, the approximations and errors derived from CFD could significantly affect the prediction of crucial parameters such as flow temperature and heat transfer. This article will present the challenges related to uncertainties in turbomachinery CFD, based on “Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines” [1]

The exact definition of boundary conditions presents one of the biggest challenges in CFD and turbomachinery given the high accuracy needed to determine the distributions of the non-uniform conditions to which turbomachinery components are subjected [2].

An additional limitation related to CFD is known as geometric uncertainty. It should be noted that, in a geometric model, a lot of details are neglected for simplicity and speed or because they are unknown, which leads to differences between the real model and the simulated one. However, even if all the details are included along with secondary air systems, they could be affected by manufacturing of the components. A study [3] quantified the change of the stage efficiency due to manufacturing errors in the rotor end-wall and to different interaction between the purge flow and the main flow.

Moreover, grid dependence analysis is a fundamental task of every numerical simulation and must be considered as such. In fact, grid spacing effects can be responsible for the poor prediction of both flow structures (i.e. von Karman Vortex Street, shock intensity and position, secondary flows…) and integral parameters such as stagnation losses. For those reasons, the effects of computational grid on the obtained results must be accounted for, when performing high-fidelity computational fluid dynamics.

Another uncertainty arises due to the improper selection between steady and unsteady simulations. For instance, when it comes to losses prediction, Pullan [4] demonstrated that a steady simulation generates 10 % less losses compared with the unsteady one. Another classical error caused by a steady simulation is the analysis of the redistribution for a hot spot in the rotor row [5].

cfd-post-processing

Along with the use of accurate boundary conditions to analyze turbomachinery flows, the simulation of component interaction is equally important. For example, an accurate methodology for the exchange of turbulence information across the interfaces is essential, especially concerning the evaluation of the turbulent length scale.

Finally, attention must be paid to the simulation of cooling devices since design is affected by geometrical uncertainty, numerical accuracy, fluid/solid interaction and boundary conditions variability [6]. It could be argued that the numerical simulation of a cooled, transonic high-pressure vane is one of the most challenging topics in CFD. Geometric uncertainty is so high that a 10 % variation of cooling hole diameter would generate an increase of 40 K in the local metal temperature of the vane [7].

Most of the described problems are related to the stochastic uncertainty, which is a function of the knowledge problem physics and the complexity of the algorithm. Then, numerical accuracy can rise with an improved knowledge of the physics and with the computational resources, while uncertainty quantification should be a strong support in the analysis and design of turbomachinery.

References:

[1] F. Montomoli et al., Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines, SpringerBriefs in Applied Sciences and Technology, DOI 10.1007/978-3-319-14681-2_2
[2] Salvadori, S., Montomoli, F., Martelli, F., Chana, K. S., Qureshi, I., & Povey, T. (2012). Analysis on the effect of a nonuniform inlet profile on heat transfer and fluid flow in turbine stages. Journal of Turbomachinery, 134(1), 011012-1-14. doi:10.1115/1.4003233.
[3] Adami, P., Martelli, F., & Cecchi, S. (2007). Analysis of the shroud leakage flow and mainflow interactions in high-pressure turbines using an unsteady computational fluid dynamics approach. Proceedings of the IMechE Part A: Journal of Power and Energy, 21. doi:10.1243/09576509JPE466.
[4] Pullan, G. (2006). Secondary flows and loss caused by blade row interaction in a turbine stage. ASME Journal of Turbomachinery, 128(3), 484–491.
[5] Butler, T. L., Sharma, O. P., Joslyn, H. D., & Dring, R. P. (1989). Redistribution of an inlet temperature distortion in an axial flow turbine stage. AIAA Journal of Propulsion and Power, 5, 64–71.
[6] Montomoli, F., Massini, M., & Salvadori, S. (2011). Geometrical uncertainty in turbomachinery: Tip gap and fillet radius. Elsevier Computers and Fluids, 46(1), 362–368. doi:10.1016/j.compfluid.2010.11.031.
[7] Bunker, R. S. (2009). The effects of manufacturing tolerances on gas turbine cooling. ASME Journal of Turbomachinery, 131, 041018-1-11. doi:10.1115/1.3072494.

The Economic Optimization of Renewable Energy

clean-blog-postGlobal warming is a very popular topic at the present time. With the upwards trend of clean technology and the realization that strict climate policy should be implemented, demand of renewable energy has sky-rocketed while conservative plant popularity continues to fall. Additionally, the number of coal power plants have significantly dropped since its peak era, as they are now known as the largest pollutant contribution, producing nitrogen, sulfur oxide and carbon dioxides.

Renewable energy comes from many sources: hydropower, wind power, geothermal energy, bioenergy and many more. The ability to replenish and have no limit on usage and application makes renewable energy implementation attractive. To make this even better, it also produces low emission. Theoretically, with the usage of renewable energy, human-kind should be able to meet their energy needs with minimal environmental damage. With growth rates ranging from 10% to 60% annually, renewable energy is getting cheaper through the technological improvements as well as market competition. In the end, the main goal is to maximize profit while minimizing our carbon footprint.  Since the technology is relatively new, capital costs are still considerably higher compared to more traditional (–and naturally harmful) implementations. This begs the question of exactly how we maximize the economic potential of a renewable energy power generation plant.

Living up to the full potential of any power generation plant starts with the design process. Solar power plants are one environmentally friendly option.  During the design process, designers should take into consideration the type and quality of the solar panels as it is important to see the economic-efficiency tradeoff before jumping into an investment. Looking into the power conversion is also one of the most important steps one should take into consideration since it would be worthless to produce more energy than what is able to be transferred and put to use and low energy generation would mean less gross income.

Geothermal power plants are another option. Many studies have shown that boundary conditions on each component play a big role in determining the plant’s capacity and efficiency. High efficiency is definitely desired to optimize the potential of a power plant and minimized the energy loss. That being said, it is important to take into account the economic sacrifice. Regardless of how good the technology is, if it doesn’t make any profit, it would not make sense for one to invest in such technology. Low capital cost but high operating expenses would hurt the economic feasibility in the long run, whereas high capital cost and low operating expense could still be risky since that would mean a higher lump sum of investment upfront which may or may not breakeven or be profitable depending on the fluctuation of energy market.

Modern technology allows investors and the engineering team to make this prediction based on models developed by the experts. SoftInWay just recently launched our economic module, so check out AxCYCLE to optimize your power plant!

Reference:
[1] http://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=4483&context=etd
[2] http://www.sciencedirect.com/science/article/pii/S0038092X12002022

Creating Vacuum – Turbo Molecular Pumps

In Physics, a “Vacuum” is defined as the absence of matter in a control volume. Generally, total vacuum is an ideal extreme condition. Therefore, in reality we experience partial vacuum where ambient pressure is different from zero but much lower than the ambient value.

Depending on the pressure we can have different degrees of vacuum, ranging from low vacuum (at 1×105 to 3×103 Pa) to extremely high vacuum (at pressures <10-10 Pa). For the purpose of comparison, space vacuum might present pressures down to ~10-14 Pa in the interstellar regions.

Vacuum is needed in research and several industrial sectors for a wide range of different applications and purposes. The main way to create vacuum is by first using primary vacuum pumps -machines that relying on the general principles of viscous fluid dynamics.

With the decrease of pressure, the distance the gas/fluid molecules will travel before they collide with each other (also called mean free path or MFP) increases. When MFP increases, it reaches a level where gas molecules are no longer interacting with each other, and the laws of continuum fluid mechanics are no longer valid.

At 1 bar, the MFP of the molecules is ~70 nm whereas in a high vacuum the MFP might increase from 10cm up to 1Km. In these conditions, we use the so-called “secondary vacuum pumps”. Though the principle of pumping a gas or fluid at very low pressure ranges is different from conventional pumps, some of them resemble the operation and design of turbopumps and are called turbo molecular pumps.

vacuum-pump
Figure 1: Schematic of a turbomolecular vacuum pump – from Wikimedia Commons

Turbo molecular pumps, introduced in 1958, are drag axial pumps (or momentum transfer pumps) used in high vacuum to pump fluid from pressures below 102 Pa. Similarly to conventional compressors, they consist of multiple stages made of a rotor and stator component. They operate transferring impulses from the rapidly moving blades to the gas molecules and pushing them towards the outlet while increasing the pressure to the one at the inlet of the backing pump.

When the molecules of the vacuum chamber enter the first stage, they are hit by the rotor blade surfaces (thin metal plates with almost no “aerofoil” features) which propels them in the stator section hitting the stator plates and moving them through the following stages. The plates’ orientation increases through the stages to adapt to the pressure variation, with some designs showing an increase of near 90 degree angles. These pumps work in parallel with primary pumps downstream (or backing pumps), which are used to bring the fluid to ambient pressure before discharging it.

holweck
Figure 2: Schematic of a Holweck stage– from Pfeiffer Vacuum

Turbomolecular pumps can work if the molecules hit by  the rotor blades reach the stator fins without colliding with other molecules. This can be achieved by reducing the gap of rotor and stator plates to be smaller than the MFP, however for manufacturing limitations, this gap is in the order 1mm. For this reason, a turbo molecular pump can work effectively when the MFP at the exhaust is of the same order of magnitude, hence exhaust pressures lower than 10Pa. Very low clearances also influence the design of the last stages of the pump. In fact, some designs may present a last stage showing a helical type channel, which is called a Holweck stage design.

To create the directed motion of the gas molecules, the rotor blade tips should move at a very high speed, so the operating rotational speeds for these machines vary from 30000 to 90000 rpm. This may create high stresses and heat due to friction in the bearing system and so consequently some exotic solutions, such as magnetic levitation bearings,  can be used with increased costs of the single unit.

A further drawback is that bigger molecules are pumped more efficiently, whereas smaller ones (such as hydrogen or helium) are more difficult to pump and remove to create a higher level vacuum. This aspect can however be alleviated by the integration of Holwech stages which increases the effectiveness of dragging smaller molecules.

 

What is an Integrated Coal Gasification Combined Cycle (IGCC) and What are the Advantages?

integrated-coal-gasification-combined-cycle-igcc
Source: http://www.slideshare.net/AbhijitPrasad4/integrated-gasification-combined-cycle-plant

Though fossil fueled power plants aren’t as commonly used anymore, coal fired power generation is still a major source of global electricity, making up about 25% of the market in total. Compared to other options in fossil fuel power generation, coal is found to be the most economical choice as well as a reliable option. Making demands that are heavily reliant on other fuels, such as oil-fired for example, slowly levers to coal power generation. The global reserve of coal can be found in abundance when compared to other energy sources (such as oil for example) as there is about 3 times more of it. Also, IGCC comes with an economic benefit as the price of coal has remained relatively constant, which results in a higher degree of confidence when relying on coal as an energy source in the future.

How Does an IGCC Work?

The system uses a high pressure gasifier to turn coal and other carbon based fuels such as high-sulfur coal, heavy petroleum residues and biomass into pressurized clean coal synthesis gas (also known as syngas). The solid coal is gas-fired to produce syngas by gasifying coal in a closed pressurized reactor with a shortage of oxygen to ensure that coal is broken down by the heat and pressure. Before going out of the system, the syngas runs through a pre-combustion separation process to remove impurities,  starting with water-gas-shift reaction to increase concentration of hydrogen and efficiency during combustion process, to a physical separation process (through variable methods). After that, a fairly pure syngas is used as a fuel in a combustion turbine that produces electricity. Waste heat contained in a gas turbine’s exhaust is used to produce steam from feed water that further turns a steam turbine to generate additional electricity.

What are the Advantages of IGCC?

IGCC is currently found to be the cleanest of coal technology with lower emission (especially for carbon dioxide by 10%) and is about 30-40 percent more efficient. Using syngas in gas turbines results in a higher output that is less dependent on temperature when compared with natural gas. Additionally, looking into the economic benefit of this technology, IGCC produces couple by-products, from chemicals to materials for industrial use that could be sold for side economic benefits.

References:

http://www.global-greenhouse-warming.com/integrated-gasification-combined-cycle-IGCC.html

https://en.wikipedia.org/wiki/Integrated_gasification_combined_cycle

 

 

Utilization of Supercritical CO2 Bottoming Cycles

In the ever-expanding market for waste-heat recovery methods, different approaches have been established in order to combat the latest environmental restrictions while achieving more attractive power plant efficiencies.  As gas turbine cycles continue to expand within the energy market, one particular technology has seen a significant upsurge due to a number of its beneficial contributions.  Supercritical CO2 (S-CO2) bottoming cycles have allowed low power units to utilize waste heat recovery economically.  For many years, the standard for increasing the efficiency level of a GTU (Gas Turbine Unit) was to set up a steam turbine Rankine cycle to recycle the gas turbine exhaust heat.  However, the scalability constraints of the steam system restrict its application to only units above 120MW.

sco2_cycle
Supercritical Co2 Cycle

HRSGs (Heat Recovery Steam Generators) are water-to-steam boilers which capture the waste heat exhaust of GTUs and convert this heat into energy in the form of high-pressure, high-temperature steam.  These systems can exist in a single or modular fashion depending on the scope of the project.  Modular HRSGs consist of any number of low pressure, intermediate pressure, and high pressure sections.  Each section allows for the extraction of gas turbine exhaust heat using separate steam drum and evaporator sections.  Even in a single pressure HRSG combined cycle, the immense amount of auxiliary equipment, the high installation costs, and the frequent maintenance necessary for such a system prevent them from providing viable heat recovery for low power GTUs.

With the introduction of a different fluid, gas turbines of small and medium size are able to utilize waste heat recovery.  Unlike steam, a supercritical CO2 system is designed to lie in the simply in the gaseous phase.  This single-phase fluid design removes the boiling process necessary for a steam system and therefore results in higher fluid temperatures and cycle efficiencies.  As well, the high energy density reduces the system component’s size and cost, and offers higher system efficiencies, reduced footprints, and significantly easier installation methods.  While all these advantages do exist within a supercritical CO2 system, working with a relatively new fluid presents different challenges that have not had the time and exposure with engineering experts as steam and gas systems have.  In particular, developing a turbine that will most efficiently run under this new fluid presents perhaps the tallest demand within the supercritical cycle. The task becomes to embrace these challenges for the benefit of higher efficiencies, lower O&M costs, and reduced greenhouse emissions.

For a more in-depth look at SoftInWay’s involvement in the S-CO2 sector, please follow this link or contact us for more information

 

References:

  1. http://www.echogen.com/documents/why-sco2-can-displace-steam.pdf
  2. http://www.softinway.com/wp-content/uploads/2015/12/IGTC2015-EvaluationOfGasTurbineExhaustHeatRecoveryUtilizingSCO2Cycle.pdf

Multi-Dimensional Coupling CFD Method for Shrouded Turbines

Tip leakage is generated inevitably by the clearance between the rotating blades and the stationary casing of a turbine, and is responsible for both the aerodynamic losses in a turbine stage and the high heat-loads in the tip region [2]. To decrease tip leakage and improve component performance, shroud seal structures have been widely applied to modern turbine components, especially to low pressure turbines, because of their advantage on both aerodynamic and structural features. However, due to the complexity of the shroud geometry, the flow structures and thermodynamic process in shroud can be extremely complicated, that is interactions of vortices, separations, jet flow, etc. Thus, because of the complex geometry of shrouds, as well as strong interactions between the tip leakage and main flow, it is not easy to draw a numerical simulation with satisfactory accuracy and time-costing in shrouded turbines. This begs the question of what should the compromise be between using simplified loss models and full 3D CFD analysis for leakage modelling?

In the main flow path of a turbine the flow will always be dominated by the blades shape, while for leakage cases the flow will be dominated by the motion and evolution of small eddies. Rosic et al. [1] reviewed the importance of shroud leakage modelling in multistage turbines. The comparison of measurements and 3D calculations shows that the flow in shrouded low aspect ratio turbines is dominated by shroud leakage. This is especially true as regards the loss distribution. The rotor shroud leakage flow greatly increases the secondary flow in the downstream stators and drives low energy fluid towards mid-span. It was pointed out that with very low values of shroud leakage the flow is reasonably well modelled by a simple 1D model of the leakage flow, using sources and sinks on the casing. However, for more representative real clearances, full 3D modelling of the seal and cavity flows is necessary in order to obtain reasonable agreement. Given that developing a simulation method with both high precision and fast solving speed is imperatively demanded for engineers to assess new designs, Zhengping Zou et al. [2] suggested that one of the potential approaches for solving the problem is a method that couples low dimensional models, 1D and 2D models, of the shroud flow with 3D (three-dimensional) simulations of the main flow passage. Specifically, some boundary source and boundary sink is set on the interface between the shroud and the main flow passage, and the source term and sink term are determined by the shroud leakage model. The schematic of this process is given in Fig. 1. The results of his study [2] demonstrate that the proposed models and methods will contribute to pursue deeper understanding and better design methods of shrouded axial turbines.

cfd
Figure 1: (a) Schematic of full 3D computation; (b) Schematic of multi-dimensional coupling simulation. [2]
 Check out AxSTREAM CFD for your designing needs!

References:

[1] “The Importance of Shroud Leakage Modeling in Multistage Turbine Flow Calculations”, Budimir Rosic, John D. Denton, and Graham Pullan, Journal of Turbomachinery, Vol 128, pp. 699-707, October 2006

[2] “Shroud leakage flow models and a multi-dimensional coupling CFD (computational fluid dynamics) method for shrouded turbines”, Zhengping Zou, Jingyuan Liu, Weihao Zhang, and Peng Wang, Energy journal, Vol 103, pp. 410-249

Feasibility of Mixed Flow Compressors in Aero Engines

The term, “mixed flow compressor”, refers to a type of compressor that combines axial and radial flow paths. This phenomenon produces a fluid outflow angle somewhere between 0 and 90 degrees with respect to the inlet path.  Referred to as the meridional exit angle, the angled outflow of this mixed flow configuration possesses the advantages of both axial and centrifugal compressors.  Axial compressors can produce higher order efficiencies for gas engines, but they have relatively low-pressure ratios unless compounded into several stages.  Centrifugal compressors can produce high-pressure ratios in a single stage, but they suffer from a drop in efficiency.  The geometrical distinction of mixed flow compressors allows for higher efficiencies while maintaining a limited cross-sectional area.  The trade-off for a mixed flow compressor when introduced to aero gas turbines is that there is an associated weight increase due to the longer impellers needed to cover this diagonal surface.  However, when related to smaller gas turbines, the weight increase becomes less significant to the overall performance of the engine.

Figure 1 - Mixed Flow Compressor Arrangement in AxSTREAM
Figure 1 – Mixed Flow Compressor Arrangement in AxSTREAM

Since the advent of more advanced Unmanned Air Vehicles (UAVs) in the 1990’s, successful integration of gas turbines into these aircrafts required high performance and lower cross-sectional areas. These requirements facilitated the introduction of mixed flow compressors as a strategic alternative. In order to analyze the feasibility of these types of compressors for aero engines, several tactics must be put in place to ensure the design is both effective and reliable. With the use of a structured database and various analysis methods, the designer can ensure an accurate study of this proposed alternative for smaller gas turbines. Design of Experiment (DoE) methods study the effect that multiple variables have on the outcome of the system simultaneously. Multiple parameters must be considered before considering this mixed flow arrangement as a feasible design. The engineer must look at the variation of the pressure ratio and flow coefficient with the meridional exit flow angle. As well, studies on the effects that different pressure ratios, meridional exit flow angles, and power variations have on the mass flow rate of the system are crucial to the design. All of these simultaneous parameters and objectives must be analyzed within a proper database to guarantee an optimized design. To learn more about the DoE optimization methods seen on SoftInWay’s AxSTREAM platform please follow this link: http://www.softinway.com/software-functions/optimization-doe/

 

References:

http://www.nal.res.in/cfdupload/Udocument/15.PDF

https://etd.lib.metu.edu.tr/upload/12611105/index.pdf

 

Exchanging Steam for SCO2

In recent days, many people find themselves spending time and resources on uncovering the best solution to optimize the power generation cycle. Until recently, 80% of power plants worldwide (whether fossil fuel, nuclear, or clean technology) used steam as its main working fluid and while it is still the most common option, today’s power plants are finding another fluid to use.

Although supercritical CO2 study began in the 1940’s, it was disregarded as an alternative fluid option because it was expensive to explore and steam was still perfectly reliable at the time. Nowadays due to increasing quantity and quality demand in power, researchers are looking into the possibility of replacing steam with supercritical carbon dioxide. The discover of this property,  increases the incentive of exploring the technology further. This year, the US Department of Energy is awarding up to $80 million towards projects to build and operate a supercritical CO2 plant.

Getting back to the basics, it is important to establish what supercritical CO2 is. SCO2 is a fluid state of carbon dioxide where it is held at or above its critical temperature and critical pressure. When carbon dioxide is heated above its critical temperature and compressed above its critical pressure, the fluid inherits both liquid and gaseous phase properties. SCO2 has many unique properties that allow the fluid to dissolve materials like a liquid but at the same time flow like a gas. It also carries the advantage of being non-toxic, non-flammable and environmentally friendly.

Supercritical CO2 is believed to improve the efficiency of thermal power plants that utilize coal, natural gas,  solar, geothermal or nuclear energy. At its supercritical state, carbon dioxide is able to generate a higher amount of electricity from the same fuel compared to a steam power plant. Accordingly , it will drop down carbon dioxide & greenhouse gas emissions as well as operating cost. The use of carbon dioxide as a working fluid also allows for the usage of smaller and more economically feasible machines. Supercritical carbon dioxide is twice as dense as steam, thus easier to compress. With this in mind, smaller components can be used, for example, to decrease the turbine size compared to a steam generating power cycle, resulting in lower costs. Although an economically feasible SCO2 plant has yet to exist due to the early stage of technology and the still high research and development costs, we may be able to expect one in the near future as it is beneficial both economically as well as environmentally compared to a traditional steam power cycle.

Optimize your SCO2 cycle and component design using AxCYCLE and AxSTREAM!

References:
http://energy.gov/under-secretary-science-and-energy/articles/doe-announces-80-million-investment-build-supercritical
https://www.scientificamerican.com/article/can-carbon-dioxide-replace-steam-to-generate-power/

An Introduction to Cavitation in Hydro Turbomachinery

A major concern for pump system engineers over the last fifty years has been caviation. Cavitation is defined as the formation of vapor bubbles in low pressure regions within a flow. Generally, this phenomenon occurs when the pressure value within the flow-path of the pump becomes lower than the vapor pressure; which is defined as the pressure exerted by a vapor in thermodynamic equilibrium conditions with its liquid at a specified temperature. Normally, this happens when the pressure at the suction of the pump is insufficient, in formulas NPSHa ≤ NPSHr, where the net positive suction head is the difference between the fluid pressure and the vapor pressure at the pump suction and the “a” and “r” stand respectively for the values available in the system and required by the system to avoid cavitation in the pump.

The manifestation of cavitation causes the generation of gas bubbles in zones where the pressure gets below the vapor pressure corresponding to that fluid temperature. When the liquid moves towards the outlet of the pump, the pressure rises and the bubbles implode creating major shock waves and causing vibration and mechanical damage by eroding the metal surfaces. This also causes performance degradation, noise and vibration, which can lead to complete failure. Often a first sign of a problem is vibration, which also has an impact on pump components such as the shaft, bearings and seals.

The vapor pressure for any liquid, is directly proportional to temperature and changes non-linearly according to the law of Clausius-Clapeyron. By regulating the pressure to which a fluid is subjected, you can change its vapor pressure and eventually make it boil at room temperature. In Figure 1 you can see the vapor pressure variation as a function of the ambient temperature for different fluids with different boiling points at  aforementioned ambient temperature.

max-blog-caviation
Figure 1: Vapour pressure – Temperature plot for several mixtures

For instance, if we take water vapor pressure at 100° C , Pa  is about 101000. However, if we reduce temperature to 5° C, the water’s vapor pressure decreases sensibly to about 872 Pa. In summary, a temperature or pressure variation will affect the boiling point of the fluid, hence its vapor pressure.
This means that the installation location has an impact on vapor pressure depending on the altitude and therefore the ambient pressure. This element should be considered on a system level to account for the possibility of cavitation occurrence.

So how can we avoid cavitation? As mentioned previously, cavitation doesn’t occur when: NPSHa > NPSHr. While NPSHa is a system parameter, the NPSHr depends on the pump design and is specified by the pump manufacturer for appropriate setup and installation of the pump within the system. The engineer should also account for a “safety” margin to avoid that unexpected fluctuations might cause the onset of cavitation.

purely  from a fluid mechanics perspective, we can define the degree of cavitation with a non-dimensional parameter called cavitation number, which is defined as seen in Figure 2:

another-formula
Figure 2

where pref  Is the pressure taken in the reference point, pv is vapor pressure, ρ is fluid density and V is the characteristic velocity of the flow. Both parameters have to be specified for each practical situation. For instance, in the case of a cavitating flow past a single foil, the reference pressure and velocity are usually chosen in a point far from the foil in the undisturbed flow. Large values of the cavitation number corresponds to non cavitating flow,  and as these  correspond to large values for the difference between reference pressure and vapour pressure.

However, these parameter results are more important when cavitation occurs, as it gives a measure of the cavitation extent. In fact, we can identify a critical value of the cavitation number σwhich corresponds to the appearance of cavitation in the flow. Considering the fully wetted flow, cavitation occurrence can be witnessed by either decreasing the reference pressure value or increasing velocity, with consequent decrease in cavitation number. Any additional reduction will lead to an additional development of cavitation within the flow. It should be noted that if reference pressure is again increased starting from cavitating flow, the cavitation disappears for σ values often higher than the critical cavitation number as a hysteresis effect can be observed.

If we look at cavitating flows within pumps and hydro-turbomachinery, we can witness very complex shapes and a wide variety of cavitation types, which can be summarized as follows:

  1. Attached cavities: In this case, cavitation appears as cavities attached to the suction side of the foil. It is called partial when the cavities covers only part of the foil or supercavity when it fully covers the suction side and closes downstream the trailing edge.
  2. Travelling bubble cavitation: this case presents isolated or small groups of bubbles depending on their nucleus density
  3. Cavitation clouds: These shows aggregates of various forms
  4. Cavitating vortices: These vortices can be more or less structured and are observed at the tip of 3D foils (or in the turbulent wake of bluff bodies)

Interactions between bubbles or with solid components, instabilities, turbulence and other phenomena can sensibly complicate the mentioned shapes and therefore the analysis of cavitation phenomena in different flow regimes within turbomachinery.

The analysis and study of cavitation can be a very difficult topic and the fluid mechanics and thermodynamics formulation to describe the connected phenomena very complex.

A thorough description can be found on the book “Fluid Dynamics of Cavitation and Cavitating Turbopumps” by L. D’Agostino, M.V.Salvetti