C.F.D. in reciprocating compressor's valves.

Tierean, Mircea ; Eftimie, Lucian ; Baltes, Liana 等

Abstract: This paper presents an application of computing fluid dynamics on the gas flow through compressor's valve. The functioning conditions of the reciprocating compressors, the model used for the computing of the viscosity coefficient of the fluid mixture are presented as well as the obtained results for the flow in the suction and discharge valves.

Key words: compressor, valve, FEA, CFD

1. INTRODUCTION

Reciprocating compressors play a major role in the chemical, petrochemical, gas, and general industry processes. Designing and implementing compressor valves and unloaders to yield improved efficiency and reliability can be complex due to many parameters that can affect performance(s). A designer must understand the flow of gas through the valves, the way the valves operate in the compressor and how reliability can be affected under a wide range of different gases compositions and operating conditions (Foreman, 1999).

The operation of the compressor is best illustrated with a pressure-volume (PV) diagram, as described in figure 1. In the diagram, [V.sub.1] represents the total volume in the compressor cylinder when the piston is at top dead center (TDC). It is known as the clearance volume. [V.sub.2] represents the volume when the piston is at bottom dead center (BDC). The swept volume is the difference between volumes at states 1 and 2. Suction and discharge pressures are shown on the vertical axis.

When the compressor piston is at state A, both the suction and discharge valves are closed, the piston is at bottom dead center and the cylinder is filled with gas at pressure [P.sub.suction]. In the next step the fluid is compressed between states A and B. When state B is reached, the valves open automatically due to a small pressure differential. The valves are assumed to fully open with a zero time delay. As the fluid is discharged to the compressor outlet, it undergoes an isobaric process until the discharge valves close due to the lack in fluid momentum and pressure differential required to keep them opened. When the valves close, the system is at state C. The fluid remaining in the clearance volume undergoes again an isentropic process until state D is reached, where the pressure differential at the inlet causes the suction valves to open.

The pressure remains constant until the piston moves past BDC and the pressure differential becomes positive again, thus closing the suction valves. At this point the compression cycle is completed. Two important measurements are related to the PV diagram:

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

* the ideal horsepower required for the compression process is represented by the shaded area "ABCD";

* the ratio between the volume of gas that enters the cylinder (point D to point A) to the swept volume (V1 to V2) is referred to as the inlet volumetric efficiency.

As illustrated in figure 2, the valve is composed by a number of circular plates, each of them pressed by springs. The plates are guided on their diameter to hold them in position over the slots in the seat. Ring valves have balanced flow through the seat, lift and exit areas, creating a lower pressure drop across the valve, which limits valve losses and increases the efficiency of the valve (Metcalf, 2000).

Conventional flat-plate designs force the gas to make two 90[degrees] turns before passing through the valve. More importantly, any impurities in gas (liquids, dirt, mechanical debris etc.) must also follow this path. At only 300 RPM, these materials have less than 100 milliseconds to pass through these turns. As a result, these inclusions often strike squarely on the valve plate at full speed, developing premature failure. These same materials pass through the ring valve with minimal impact on the radii disc.

2. VISCOSITY MODEL

More often than note, the fluid processed by the compressor is a complex mixture of chemical nonreacting compounds, usually hydrocarbons. A detailed analysis of the fluid flow through the compressor valves requires accurate knowledge of the transport properties of the mixture. Among these, the dynamic viscosity and thermal conductivity are of importance (Harvard Lomax et al., 2001; White, 2001).

The mixture laminar viscosity is calculated using the Wilkes' mixing model (Wilke, 1950). First, the viscosity coefficient is computed for each individual species n using Sutherland's law, as follows:

[[mu].sub.n]/[[mu].sub.0] = [(T/[T.sub.0]).sup.3/2] [T.sub.0] + S/T + S; (1)

where T is the local static temperature, and [[mu].sub.0], [T.sub.0], and S are constants for each specie n.

For N total species, the individual viscosity coefficients are combined using

[[mu].sub.mixt] = [summation over i] [x.sub.i][[mu].sub.i]/[summation over j]([x.sub.i][[phi].sub.i,j]); (2)

where [[phi].sub.i,j] is the mixing coefficient computed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

In the previous relation ii is the dynamic viscosity and [M.sub.i] is the molar mass of each component of the flowing gas.

The same model was used to obtain the thermal conductivity of the flowing gas:

[[lambda].sub.mixt] = [summation over i] [x.sub.i][[lambda].sub.i]/[summation over j]([x.sub.i][phi][cond.sub.i,j]); (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

where [[lambda].sub.i] is the thermal conductivity of each component of the flowing gas and a=1.

3. RESULTS

This study refers to the valves of the first stage of the 285 mm diameter compressor, with the pressures [p.sub.suction] = 12 bar, [p.sub.discharge] = 28 bar and temperatures [t.sub.suction] = 38[degrees]C, [t.sub.discharge] = 118 [degrees]C.

Figure 3 shows the 3D model of the fluid velocity in the suction valve. The maximum speed is 51.6 m/s. In figure 4, the fluid velocity vector is presented and figure 5 shows the pressure map in the same valve. The fluid velocity vector in discharge valve is presented in figure 6.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

The F.E.A. was done using CFX 5.7.1 and Ansys Workbench 9.0.

4. CONCLUSION

This method is very useful to study the fluid flow in valves in the design process.

Having the values of the velocities and pressure, the designer can establish the adequate dimensions of the suction and discharge channels and holes, the value of the closing element lift and the contact areas.

An important parameter determined from the CFD analysis is the pressure drop across the valve. The designer may choose to minimize it in order to allow for lower input work requirement and thus better compressor efficiency while considering the geometrical restrictions imposed by the compressor.

5. REFERENCES

Foreman, S. (1999). Compressor Valves and Unloaders for Reciprocating Compressors. Dresser-Rand, New York

Harvard Lomax, H.; Pulliam, T.H. & Zingg, D.W. (2001). Fundamentals of Computational Fluid Dynamics, SpringerVerlag, ISBN 3-540-41607-2, Berlin

Metcalf, J.R. (2000). Effects of Compressor Valves on Reciprocating Compressor Performance. Stafford. Cook Manley, TX

White, F.M. (2001). Fluid Mechanics, McGraw-Hill ISBN, 9780072831801, New York

Wilke, C.R. (1950). A Viscous Equation for Gas Mixtures, In: Journal of Chemical Physics, pp. 517-519, Vol. 18