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a level where gas molecules are no longer interacting with each other, and the laws of continuum fluid mechanics are no longer valid.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.

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.

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.


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.


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:


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

Mixed Flow Pumps

As with any turbomachinery, pump design requires a lot of effort on finding the right blade profile for the specified application. As there is no right or wrong in the process, engineers have to make some general assumptions as a starting point. Generally, we can say that the focus of this task is to minimize losses. It is obvious that the selected blade shape will affect several important hydrodynamic parameters of the pump and especially the position of optimal flow rate and the shape of the overall pump performance curves. In addition to axial and radial pump design in recent years, we also have seen the development of mixed-flow pumps. A mixed flow pump is a centrifugal pump with a mixed flow impeller (also called diagonal impeller), and their application range covers the transition gap between radial flow pumps and axial flow pumps.

Let’s consider a dimensionless coefficient called “specific speed” in order to be able to compare different pumps with various configurations and features. The “specific speed” is obtained as the theoretical rotational speed at which a geometrically-similar impeller would run if it were of such a size as to produce 1 m of head at a 1l/s flow rate. In formulas:
formulawhere ns is the specific speed, n the rotational speed, Q is the volume flow rate, H is total head and g is gravity acceleration.

Fig1: Picture courtesy of KSB Pumps

The specific speed for mixed flow pumps might go from ns=30  to ns=80  for low-speed mixed flow pumps and can increase between ns of 80 and 160  for higher speed mixed flow pumps, as shown in Fig 1 to the left.

As you can see, Mixed-flow pumps have specifics speeds right in-between radial and axial configurations. For mixed flow pumps we can mainly see two casing configurations. In case of low peed pumps, the most appropriate configuration is the volute casing, which shows big similarities with centrifugal pump designs. However, for higher specific speeds raising above the ns =~130/140  value, we see configurations combining the  mixed flow impeller with a diffuser + tubular casing. This solution is chosen to avoid the unreasonably large volute outlet cross sections that would be required to maintain the flow due to the very low tangential component of the absolute velocity at the impeller outlet.

Fig2: Picture courtesy of Sulzer Pumps

Mixed-flow pumps with tubular casing are often installed in a vertical arrangement, and can be found in multistage configuration for high flow applications, such as irrigation, urban water supply, thermal power plants etc.

In a nutshell, the advantage of mixed-flow pumps over the “competition” is to be a “jack of all trades”. They combine higher massflow of axial configurations with higher pressure achievable by centrifugal machines.


Exotic Turbomachinery – Viscous Disc Pumps

Turbomachinery can be divided into two main groups. Group one consists of machines that perform work on the fluid, requiring energy and increasing its pressure, such as compressors, pumps, and fans. Group two consists of those that extracts energy from the fluid flowing through it – for example, wind, hydro, steam, and gas turbines.

Pumps specifically are devices whose purpose is to move fluid at a constant density, increasing its kinetic energy and its pressure while consuming energy in the process. We are quite used to seeing centrifugal and axial pumps, as they are the most common configurations.  However, more exotic designs have been tested and developed throughout the history of fluid machinery.

VTeslaiscous disk pumps are one such design – inspired by the concept of Tesla Disc Turbine, and conceived and developed in 1913. The key feature of these turbines is the bladeless design, consisting of multiple parallel rotating discs within a casing. Additionally, its operating principle is based in the so-called boundary layer effect. The main difference from a conventional turbine design is that there is no impingement of the rotating parts on the fluid.

As shown in figure 1, the nozzle is inserting the fluid to the discs’ edge, which is dragged by the moving fluid through its viscosity and fluid adherence to the discs’ surface. After energy is transferred to the discs, the fluid gets extracted by the center exhaust.

The same set of discs and a slightly different shape of casing/volute can be used as a pumping device, which is also called a boundary layer disc pump.

Even if Tesla’s turbine design didn’t undergo further development, the disc pump design found its purpose in highly demanding pumping applications.


In the last 30 years this type of pump has found its niche in high viscosity fluids and low Reynolds number flows. For instance, common applications include the pumping of crude oil, sludge, food pulps and wastewaters. They offer excellent pumping capacity for fluids with enthralled gases or delicate solid particles.

Due to its operating principles, flow is similar to an ordinary pipe with parabolic velocity profiles and stationary layers of fluid (relative to the rotating discs). This allows enthralled gases or solid particles to remain located in the core of the flow with no contact to the discs. As such, the reliability and lifetime for these pumps is very high, as the moving parts show little to no deterioration and require minimal maintenance.


In these conditions, viscous pumps show much higher efficiency despite the lower level of complexity when compared to their conventional counterparts with centrifugal design. Less complexity means lower maintenance and lower costs.

Simplicity of the design in these pumps also shows promising application in microfluidics with different miniaturized designs for drugs transportation and biomedical applications, such as blood transportation with no damage to plasma particles. Also in these operating conditions with low Reynolds flow, disc pumps have shown efficiencies as high as 95%, much higher than a centrifugal or displacement counterpart. Different designs have been investigated and proposed, involving 1, 2 or more bladed discs, depending on the application and size.

Despite of the advancements in the design of turbomachinery, and the increase in computing power allowing more and more complex fluid dynamics analyses, viscous disc pumps remain a unique case that shows that complexity and over-development do not necessarily equal higher efficiency and performance.


“Single-Disk and Double-Disk Viscous Micropump” – D. Blanchard, P. Ligrani and B. Gal – Sensors  and Actuators A-Physical, 122, 149-158, 2005

“Analytical and experimental modeling of a viscous disc pump for MEMS applications” – Marco D. C. Oliveira and José C. Páscoa

5 Steps to Advanced 3D Blade Design

3 Blade Design

To decrease losses and increase performance of a turbine, we need to develop special (compound) geometries. Here’s your turbomachinery cheat sheet to advanced 3D blade design!

1. Optimizing plane profiling

There are several positive things that can give proper plane sections profiling: decreasing the profile losses, decreasing secondary losses and satisfying structural limitations. Continue reading “5 Steps to Advanced 3D Blade Design”

3 Categories and Sources of Vibrations

In view of the large number of blades in any turbine machine, the existence of unavoidable sources of vibration excitation and the serious consequences of the failure of just one blade, an intimate knowledge and understanding of the vibration characteristics of the blades in their operating environment is essential.

Vibration excitation can arise from a variety of sources but principally involves the following categories: Continue reading “3 Categories and Sources of Vibrations”

Calculating Sections in Steam Turbines

9 Section Axial Steam Turbine
9 Section Axial Steam Turbine

What’s a better way to begin our brand new turbomachinery blog then by addressing a common design question about something we are very familiar with – steam turbines?

Many times the question, “How many calculation sections do you recommend for the (insert any number here)-stage steam turbine?” travels through our tech support emails and we always answer our clients with what we think is best practice. Continue reading “Calculating Sections in Steam Turbines”