experimental and numerical analysis of reed valve movement

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International Compressor Engineering Conference School of Mechanical Engineering

2021

Experimental and Numerical Analysis Of Reed Valve Movement In Experimental and Numerical Analysis Of Reed Valve Movement In

An Impact Fatigue Test System and Reciprocating Compressors An Impact Fatigue Test System and Reciprocating Compressors

Muhammad Waqas Tofique Voestalpine Precision Strip AB, [email protected]

Alexander Löf Voestalpine Precision Strip AB

Eugenio Schillaci Termofluids

Pablo Castrillo Universitat Politècnica de Catalunya - Barcelona Tech (UPC)

Joaquim Rigola Universitat Politècnica de Catalunya - Barcelona Tech (UPC)

Follow this and additional works at: https://docs.lib.purdue.edu/icec

Tofique, Muhammad Waqas; Löf, Alexander; Schillaci, Eugenio; Castrillo, Pablo; and Rigola, Joaquim, "Experimental and Numerical Analysis Of Reed Valve Movement In An Impact Fatigue Test System and Reciprocating Compressors" (2021). International Compressor Engineering Conference. Paper 2697. https://docs.lib.purdue.edu/icec/2697

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1613, Page 1

Experimental and numerical analysis of reed valve movement in an impact fatigue test

system and reciprocating compressors

Muhammad Waqas TOFIQUE1*, Alexander LÖF1, Eugenio SCHILLACI2, Pablo CASTRILLO3,

Joaquim RIGOLA3

1voestalpine Precision Strip AB, Research & Development,

Munkfors, Sweden

2Termofluids,

Av. Jacquard 97-E, 08227 Terrassa, Barcelona, Spain

3Universitat Politècnica de Catalunya - Barcelona Tech (UPC),

ESEIAAT, C/ Colom, 11 - 08222 Terrassa (Barcelona), Spain.

* Muhammad Waqas Tofique

E-mail: [email protected]

ABSTRACT During operation of a reciprocating compressor, its flapper valve opens to allow the passage of gases and closes by

striking against the valve impact plate. This reed valve movement and impact is repeated billions of times. This

cyclic movement has a significant influence on the impact fatigue life of the reed valve and, hence, the lifetime of a

compressor.

Inside a reciprocating compressor, a number of parameters including: the valve design, valve material, compressor

operating frequency and suction/exhaust pressure, influence the reed valve movement. The valve movement can be

defined in terms of valve frequency, valve lift, valve velocity and impact velocity. These response parameters

heavily influence the compressor efficiency and impact fatigue life of reed valves.

In this paper, we first studied the valve movement parameters for a reed valve design using an experimental test

setup. In experimental testing, the valves were excited into movement using air pressure pulses at 100 Hz frequency

(air pulse width of 5 milliseconds). The valve movement was recorded by a laser sensor at 10 000 frames per

second. The operating conditions such as the operating frequency, air pulse width, applied pressure and airflow rate

were measured. The valves were not tested to failure but only to collect the dynamic data of valve movement such as

the valve movement curve (valve displacement vs time), average valve lift and reed velocity data.

The experimental results were employed to validate a complex in-house 3D CFD finite-volume model aimed at

studying in detail the valve and gas dynamics, whose interaction is solved by means of a Fluid-Structure Interaction

(FSI) algorithm. The complete valve movement curve obtained from simulations – reed valve displacement vs time

– correlated with that obtained from the experimental tests with small error. Similarly, the difference in experimental

and numerically obtained average valve lift and impact velocity values were quite small for practical purposes.

Finally, fluid-dynamic results for pressure and impact forces were employed to feed a finite-element based code

aimed at studying the structural behavior of the reed vale. Bending fatigue and impact fatigue stresses induced in the

reed valve during its movement cycle were calculated. The magnitude of stresses and their positioning was

determined, which correlated with the commonly observed areas of fracture initiation in these valves.

The numerical models, as well as the information obtained from this study will help the compressor manufacturers

to design their compressors to enhance efficiency and reed valve’s reliability. This type of information is not readily available from a working compressor.

1. INTRODUCTION Significance of the reed valve movement can be judged by its influence on the impact fatigue and bending fatigue

life of the reed valve. Long impact fatigue and bending fatigue lives are essential for the reliable operation of a

25th International Compressor Engineering Conference at Purdue, May 24-28, 2021

mailto:[email protected]

1613, Page 2

compressor and, hence, the operation of any appliance that the compressor is installed in. In addition, the valve

movement parameters, such as valve lift, affect the coefficient of performance (COP) of a compressor. On the other

hand, higher valve lift would mean higher reed velocities due to the elastic restoring force, hence, higher impact

intensities when the valve shuts down and strikes against the valve seat. The higher impact intensities would mean

higher impact fatigue stresses are generated inside the reed valve body after the impact. Similarly, higher bending

fatigue stresses would be generated in the reed valve body when the valve lift is higher. There have been numerous

theoretical studies in the past such as Pandeya (1978) and Böswirth (1980) that discussed the dynamic behavior of a

generic geometry of reed valves and the impact stress state generated due to the valve striking against the impact

seat. However, a deeper analysis of the reed valve movement and the resultant stresses generated in the reed valve

body is required to design safe and reliable compressors.

The interaction between a reed valve and the gas flowing through it can be characterized entirely by computational

fluid dynamics (CFD), and, more specifically, by means of fluid structure interaction (FSI) algorithms. In addition,

valve internal stresses due to external forces can be evaluated in detail by means of Computational Solid Dynamics

(CSD).

A numerical set-up capable of fully simulating the behavior of the gas and its mutual interaction with a valve

includes a certain number of numerical issues whose complexity makes the methodology not yet fully reliable. Some

of the problems that must be solved concern: (1) the difficulty in mutually coupling a structural solver for studying

the stresses operating in the valve with the external forces exerted by the fluid; (2) the representation of the impact

between the valve and the base, with the corresponding 'disappearance' of control volumes which requires the use of

numerical techniques such as re-meshing or immersed boundary for the representation of the solid; (3) detailed

representation of all the physical phenomena that characterize the process, as flow topology, turbulent effects,

backflow, fluttering and collisions, among others. The previously mentioned problems also introduce strict

requirements from the point of view of computational cost, making such simulations expensive as well as complex.

Some examples of resolution of valve dynamics by means of CFD and FSI techniques already exist in the literature.

For instance, Mayer et al. (2014) and Tao (2018) carried out a validation of FSI computational methods by

reproducing experimental results of reed valves. Furthermore, the FSI numerical prediction has allowed

investigating the effect of gas velocity, valve thickness and other geometrical parameters on the process efficiency

as shown by Coskun et al.(2016), Gasche et al. (2016) and Wu et al. (2016). The numerical method used in this

work was developed on the Termofluids’ in-house platform and verified for the framework of reed valves in

Gonzalez et al. (2016) and González et al. (2019). The numerical method consists of a combination of a finite

volumes solver for the resolution of the flow on an unstructured mesh with a solver for the valve movement. The

interface between gas and valve is represented by a moving mesh while the forces are integrated on the valve

through a normal mode superposition method with penalty forces to represent the impact between valve and base.

Regarding CSD, it is possible to find works in the literature that simulate and analyze valves using the Finite

Element Method (FEM), in some cases commercial software are used such as in Yu et al. (2017), Lajús Junior et al.

(2013) and Yu et al. (2018); while in others in-house codes are developed such as in Lee & Son (2008) and Nilsson

et al. (1980). Generally, the displacement of the valve, the impact velocity of the valve when it strikes the seat and

the impact stress are points of interest in those works. Regarding the impact stresses, in some cases the Von Mises

stresses are studied, see Nilsson et al. (1980); and in others the principal stresses, see Yu et al. (2017) and Lajús

Junior et al. (2013). In this work a code is developed using the FreeFEM ++ tool (Hecht, 2012) to analyze the

stresses within the valve, how these stresses are modified by the impact with the seat and the characterization of the

impact force when it appears. In this simulation, only the solid is studied using the pressure generated by the fluid as

a boundary condition. Likewise, in this code the impact force is implemented using the penalty method (Armero &

Petőcz, 1998).

In the current work, the parallel development of an experimental campaign together with the numerical one, with

experiments designed ad-hoc and easily replicable, allow a sure advance towards maturity in the use of CFD-FSI

methods for the study of valve dynamics, as well as interesting insights about valve dynamics and stresses

distribution, carried out by means of CSD.

2. EXPERIMENTAL

Reed valve movement experiments were conducted on a custom-built impact fatigue test rig that, in normal

operation, uses air pulses to produce movement of the valves at a range of frequencies (Hz) and pulse widths

(milliseconds). The frequency, and pulse-width, is provided as input to the control software on the connected

computer.


Compressed air storage tank Computer with control software

AirFlow meter ____. ____.

Air Pressure Regulator

____.

1613, Page 3

A schematic sketch of this custom-built impact fatigue test rig is shown in Figure 1. A dedicated compressor

provides compressed air at up to 13 bars pressure. This compressed air gets stored in a storage tank. The compressed

air is transferred through tubes of 4 mm inner diameter and passes through a flow meter that measures the airflow

rate in liters per minute. The air pressure regulator regulates the magnitude of the compressed air pressure before it

passes through a high frequency solenoid valve. There is a provision to increase or decrease the magnitude of

pressure supplied to the solenoid valve, and hence the airflow rate, through the pressure regulator. The compressed

air pressure reported in this paper is measured at the solenoid valve opening.

The reed valve was made to strike the valve plate repeatedly inducing impact fatigue stresses in them, hence,

mimicking the movement of a reed valve in an actual compressor. A laser sensor measures the reed valve’s displacement, and thus velocity, and its operating frequency at a sampling rate of 10000 per second. This data is

displayed and stored on the control software.

Figure 1: Schematic drawing of the working of the custom-built impact fatigue test system available at voestalpine

Precision Strip AB, Sweden that was used to test the reed valve (test specimen) movement in this study.

In the custom-built impact fatigue test system, one crucial component that influences the reed valve movement is the

high frequency solenoid valve. It is a two-way, in-line valve that is electrically actuated with moulded-in cable.

Installed in the impact fatigue test system, it receives compressed air after the pressure regulator and through its fast

switching action coverts it into pressurized air pulses of fixed frequency and pulse-width. These pressurized air

pulses are then supplied to a reed valve/test specimen that moves in response. A schematic representation of the

switching behavior of the solenoid valve for a trigger pulse-width of 5 milliseconds is shown in Figure 2. It shows

that the solenoid valve takes about 1 millisecond to switch on as the electric current flows through the moulded-in

wire and into the solenoid coil. As the solenoid valve opens the compressed air pushes through a small opening as

the pressure starts to rise to reach its maximum value of 6 bars; the air pressure then stabilizes for approx. 3

milliseconds before the valve switches off; the valve switching off time delay is approx. 0.6 milliseconds; as the

solenoid valve starts to close the pressure starts to reduce to its minimum value. This pulsing cycle was repeated a

few thousand times as the reed valve movement data is recorded on the control software.


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Figure 2: Schematic representation of the switching behavior of the high frequency solenoid valve provided by its

manufacturer for compressed air pressure of 6 bars.

2.1 Test specimen design The geometry of the reed valves tested in this work is presented in Figure 3. This reed valve design was chosen as it

is a simple and efficient design that is quite common in the compressor industry. The reed valves were produced by

photo-chemical etching process along the rolling direction. The reed valves were not subsequently tumbled. In the

impact fatigue test system; the reed valve was mounted using a steel die that covered a part of its length. The

measuring point of the laser detecting valve movement data was 2.5 mm from the top edge of the valve head along

the centerline.

(a) (b)

Figure 3: a) The geometry and dimensions of the reed valve specimens used in this study, (b) the reed valve as

tested in the impact fatigue test system.

The reed valves were manufactured from 0.203 mm thick strip of Flap-X steel grade. Flap-X is a martensitic

stainless steel that is hardened and tempered to achieve a combination of high tensile strength, ductility and high

cleanness that are vital for good impact fatigue and bending fatigue properties. The nominal chemical composition

of Flap-X is shown in Table 1.

Table 1. Nominal chemical composition (wt. %) of the Flap-X steel grade used for the reed valve specimens

Steel grade C Si Mn Cr Mo P S

Flap-X 0.38 0.45 0.55 13.5 1.00 ≤0.025 ≤0.015


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1613, Page 5

3. NUMERICAL APPROACH

3.1 CFD-FSI methodology

The CFD problem consists in solving the Navier-Stokes equations in the incompressibility limit. In the model, a

Newtonian behavior of the fluid and constant thermophysical properties was assumed. With these hypotheses, the

governing equations can be written as follows.

(1)

The various magnitudes are listed here: V air velocity [m/s], t time [s], p air pressure [Pa],air density [kg/m3],

air viscosity [Pa·s].] The compressed air is characterized by = 8.5 kg/m3, = 18.3e-6Pa·s. The numerical

simulations described in this section are carried out with the unstructured parallel CFD code TermoFluids (see

Termofluids webpage). Large-Eddy Simulations (LES) are carried out: a Sub-Grid Scale (SGS) model is applied in

order to represent the smallest scales, while only the larger eddies are explicitly solved. The chosen SGS scheme is

the Wall-adapting local eddy-viscosity (WALE) model. The Navier-Stokes equations are solved by means of a

Fractional Step Method and advanced in time with an explicit scheme, yielding the air velocity field at each time

step. The domain is represented in a simplified way in Figure 4(a), accounting for an inlet port where a variable inlet

flow rate is imposed, and lateral outlets with pressure-based conditions are set to mimic the flow discharge. The

other walls are solid walls boundaries. The base mesh is an unstructured tetrahedral mesh composed of around 300k

cells and represented in Figure 4(c). At each time step, the mesh undergoes deformations to adjust the position of the

internal points, thus, accommodating changes in the domain boundaries (upper and lower ones) without involving

topological alterations. In order to avoid a remeshing procedure when valve is closed, some elements of the mesh

perform as solid by using an immersed boundary method (IBM), as represented in Figure 4(b). The motion of the

valve (i.e. the boundaries limiting its surface) is modeled by means of the Kirchoff-Love plate theory, valid for

arbitrarily shaped plates with uniform thickness h. The displacement of this vibrating system can be obtained from a

combination of M free vibration modes, as where <f>(x,y) and qm are the normal

deformation pattern and the generalized coordinates corresponding to the vibration mode m , respectively. Normal

deformation patterns are obtained by means of a commercial software by solving the eigenvalue problem of the free

vibration equation of the system while qm are obtained from the Kirchoff-Love equation by applying the external

stresses to the plate (fluid pressure and shear stress, gravity, impact force). More details about the whole CFD-FSI

method are given in González et al. (2019). A semi-implicit approach for strongly coupled problems developed by

Naseri et al. (2018) is employed to solve the fluid-solid interaction.

Figure 4: (a) Schematic of the CFD-FSI set-up; (b) Deformed domain with valve fully open; (c) unstructured mesh

and detail around the valve boundaries.


1613, Page 6

3.2 Solid analysis methodology The Cauchy moment equations are solved in order to study the solid dynamics and its internal stresses. In this case it

is assumed that the material is homogeneous, has a linear elastic behavior and geometric non-linearity effects are not

considered. Likewise, volume forces are not considered. With these hypotheses the equation reduces to:

(2)

where p = 7700 kg/m3 is the density, u is the displacement and q is the Cauchy tensor. With the aforementioned

hypotheses Cauchy tensor is related to the displacement by means of the constitutive equation a = 2µ e + l e

where is the infinitesimal strain tensor and µ and are the Lamé’s material parameters related to

the most common Young’s modulus E = 220264 MPa and the Poisson’s ratio V = 0.28 ;

A = d = ( lEv an .

( + v)( l - 2v) _

µ 2( 1E+_v) )

In order to solve this differential equation, boundary conditions are necessary. In that sense, it is known that the

valve is held at one end (displacement conditions), while Neuman conditions are imposed on the other surfaces, in

terms of fluid pressures and impact forces. For the fluid pressure p , obtained from the CFD-FSI simulation, the

boundary condition is a · n = p where n is the outward normal of the solid. The condition for the impact force is

similar to the fluid pressure but it depends on the valve displacement that makes it a non-linear condition. To solve

this problem it is necessary to solve the unilateral contact constraints and the persistency condition (Armero &

Petőcz, 1998). For this formulation it is necessary to choose two penalty parameters and , in this work

kP = 5000 kPa/mm = 1000 kg/mm2 and mp . For the simulation, a code was developed in the FreeFEM++ tool

using an HHT scheme ( a -method) for the temporal integration with the parameters a = 0.51 , f3 = 0.555025 and

y = 0.99 (Armero & Petőcz, 1998).

4. RESULTS

4.1 Experimental results from the impact fatigue test system In the impact fatigue test system, a frequency of 100 Hz and pulse-width of 5 ms was specified in the control

software. This meant that compressed air pulses of 100 Hz frequency were created by the solenoid valve whose

characteristic switching behavior is shown by the schematic representation in Figure 2, albeit for slightly higher

maximum pressure of 7.2 bars.

The reed valve displacement that occurred in response to the compressed air pulses of 100 Hz is shown in Figure 5.

As the solenoid valve was about to open the compressed air pressure started to mount that reached its maximum

value when the solenoid valve was fully open and then reduced to lower pressure magnitude as the solenoid valve

closed. In response to the applied compressed air pulses, the reed valve started to move away from the valve seat – see the valve seat position at approx. -3,90 mm indicated by a dashed line in Figure 5 to reach its maximum opening

amplitude. The reed valve then closed due to elastic spring force as it acted against the compressed air, since the

solenoid valve was still open. As the reed valve struck against the valve seat, it bounced up twice partly under the

action of the compressed air. As another compressed air pulse arrived at the reed valve, this movement cycle was

repeated again. However, it can be seen in Figure 5 that there are slight differences in the magnitude of the reed

valve amplitude that occur due to local differences in air pressure, airflow rate and obliqueness of the reed valve

during its movement – especially after it bounces back from the impact seat.


1613, Page 7

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0 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0,04 0,045 0,05

Time (seconds)

Pressure (Bars)

Reed displacement (mm)

Trigger

Solenoidvalve open

Solenoidvalve open

Solenoidvalve open

Solenoidvalve open

Solenoidvalve open

Solenoidvalve closed




Valve seat position

Figure 5: Reed valve displacement plotted as a function of time for input frequency of 100 Hz and pulse-width of 5

milliseconds specified to the solenoid high frequency valve.

4.2 Numerical simulation results

4.2.1 CFD-FSI results:

The study simulated the evolution of the flow and the movement of the valve during an entire valve stress cycle,

which lasts 10 ms (Airflow pulse 100 Hz). The flow imposed at the entry of the domain mimics the air pulse of the

experimental set-up. It grows rapidly and remains constant for a certain period, and then gradually decreases to 0 at

t=4 ms from the beginning. The inlet flow rate evolution along a cycle is reported in Figure 6 (a). During the rest of

the cycle, the valve opens and closes twice, rebounding against the base. The results in Figure 6 show a good

agreement between numerical (CFD-FSI) and experimental data, both in terms of valve lift and displacement. This

is especially true when considering that the experimental signal is a 'typical' one, as certain variability is visible

between successive cycles, as visible in the displacement signal reported in Figure 5. Differences between the two

results can be seen in the descent phase after the first opening. In fact, the numerical curve shows a deflection,

probably due to the fact that the incompressible gas in the inlet duct acts as an obstacle during the valve closure.

Another difference can be noticed (in the valve velocity curve in Figure 6b) at the point of the first impact: in the

experimental signal a certain plateau can be noticed, probably due to the flexion of the valve when it comes in

contact with the base, while in the simulation the contact is practically 'instantaneous' (sudden velocity increase).


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1613, Page 8

Figure 6: Numerical (CFD-FSI) vs experimental results for: (Left) valve lift, (Right) valve velocity.

4.2.2 Results of Finite Element Analysis:

The solid simulation in FreeFEM++ uses the pressure obtained from the FSI simulation carried out in TermoFluids.

A verification of the outputs of the CSD method i.e. valve lift and velocity, also shown in Figure 6, are calculated. 3The first impact occurs in the time interval t = ( 4.453, 4.579) e - s and the second impact at

t (6.923, 7.122)e- 3 s. These time intervals correspond to the instants (460 - 480) and (768 - 790) of the

simulation respectively. Figure 7 show the impact pressure Cp and the impact force FCp for each of these instants.

Figure 7: Maximum value of Cp and impact force FCp for each instant: (Left) first impact; (Right) second impact.

Before impact, the maximum stresses in the valve are due to its bending provoked by the fluid pressure and they can

be found in the neck of the valve. Subsequently, due to the impact, it is observed that the maximum and minimum

stresses are found at the tip of the valve increasing the Von Mises stress. Figures 8-9 show the Von Mises equivalent

stress ( ) in the lower fibres for both impacts.

Figure 8: Von Mises stress in the first impact.


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1613, Page 9

Figure 9: Von Mises stress in the second impact.

Four points on the valve tip were analysed to study the temporal evolution of the aforementioned stresses in the

lower fibres of the valve. In Figure 10 it is possible to see that in all the points studied, the impact clearly generates a

change in the stresses. Likewise, at the points 2 & 3 in Figure 10a where the valves usually fail – see Figure 10c – relatively higher stresses are noted, see Figure 10b.

a b)

c)

Figure 10: (a) Points studied at the valve tip; (b) Envelope of Von Mises stress σvm; c) failed reed valves in impact

fatigue experiments.

6. CONCLUSIONS

Based on the work done in this study it can be concluded that the model delivered reasonably accurate results for the

reed valve operating at 100 Hz frequency, taking into account the high variation in the experimentally measured

results. The valve displacement and velocities obtained with the simulations correlate accurately enough for

practical purposes with the experimental results. The obtained bending stress has a reasonable magnitude and is

located in the expected area in the valve. For the impact stresses, it is seen qualitatively how the stresses increase

significantly at the impact as the stresses travel in the valve body in the form of waves starting from its tip. The

position of failures of the valves in the experimental results correlates with concentration of the higher magnitude of

impact fatigue stresses in the valve after the point of time of the valve impact against the valve seat. The CFD and

CSD models, in their current form, can be employed by compressor designers to study valve dynamics for other

parameters such as valve thickness, valve design and physical properties.


1613, Page 10

ACKNOWLEDGEMENT

This research was made possible through funding and support by voestalpine Precision Strip AB, Sweden.

Special thanks is extended to our research partners in this project at Termofluids and Universitat Politècnica de

Catalunya - Barcelona Tech (UPC).

REFERENCES Armero, F., & Petőcz, E. (1998). Formulation and analysis of conserving algorithms for frictionless dynamic

contact/impact problems. Computer Methods in Applied Mechanics and Engineering, 158(3-4), 269-300.

Böswirth, L. (1980). Hypothesis on the failure of spring loaded compressor valve plates. Proceedings of the

International compressor engineering conference at Purdue, Purdue University (198-206), Paper 332.

Indiana, USA.

Coskun, U. C., Gunes, H., & Sarioglu, K. (2016). A numerical model of fluid structure interaction of a fluttering

valve. In Proceedings of the 5th International Conference on Jets, Wakes and Separated Flows

(ICJWSF2015) , 421-429.

Gasche, J. L., Dias, A. D., Bueno, D. D., & Lacerda, J. F. (2016). Numerical simulation of a suction valve:

comparison between a 3D complete model and a 1D model. International Compressor Engineering

Conference (Indiana).

Gonzalez, I., Lehmkuhl, O., Naseri, A., Rigola, J., & Oliva, A. (2016). Fluid-structure interaction of a reed type

valve. International Compressor Engineering Conference (Purdue).

González, I., Naseri, A., Rigola, J., Pérez-Segarra, C. D., & Oliva, A. (2019). Detailed prediction of fluid-solid

coupled phenomena of turbulent flow through reed valves. In IOP Conference Series: Materials Science

and Engineering, Vol. 604, No. 1, p. 012064.

Hecht, F. (2012). New development in FreeFem++. Journal of Numerical Mathematics , 20(3-4), 251--265.

Lajús Junior, F. C., Deschamps, C. J., & Alves, M. (2013). Numerical analysis of seat impact of reed type valves.

8th International Conference on Compressors and their Systems, 555-563.

Lee, Y., & Son, S. (2008). Study on the Fatigue Strength of a Suction Flapper Valve Used in a High Efficient

Reciprocating Compressor. International Compressor Engineering Conference(1913).

Mayer, J., Bjerre, P., & Brune, F. (2014). A comparative study of different numerical models for flapper valve

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