geometric scaling

7/23/2019 Geometric Scaling

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IMPACT OF GEOMETRIC SCALING ON

CENTRIFUGAL COMPRESSOR PERFORMANCE

Jay M. KochPrincipal Engineering Leader

Dresser-Rand CompanyOlean, NY, USA

ABSTRACT

Compressor performance for liquefied natural gas (LNG) main refrigeration units is very important due to the

direct link between compressor efficiency and LNG production for a fixed amount of power. Dresser-Rand

recently designed a series of new stages for the LNG market that provided improved efficiency and a wider

range of operation.

Industry practice is to rig test new stages prior to application in production units. For LNG main refrigeration

applications the production compressor can be very large with impeller diameters up to 2.0m (78.74 inches).

Rig testing is often done at a reduced size instead of the production size to minimize cost and cycle time.

Test similitude is achieved for flow coefficient and tip Mach number by direct scaling of the production

compressor geometry, but the Reynolds number is often not preserved. The resulting test rig performance

does not duplicate the performance of the production unit.

The objective of this paper is to document the impact of scaling and Reynolds number on compressor

performance. The paper details rig testing completed to validate analytical design tools. Test results are

shown for a series of impellers, at conditions typical for LNG main refrigeration compressors for both the

production size and reduced size. The test results are compared with analytical predictions from

Computational Fluid Dynamics, (CFD). A discussion is offered on how CFD can be used to predict the

scaling impact, thus allowing high confidence in the performance prediction when reduced size testing is

completed.

INTRODUCTION

There are many different process cycles that can be selected to convert natural gas to liquid form. These

include Air Products AP-M (single mixed refrigerant), AP-C3MR and AP-X, ConocoPhillips Optimized

Cascade process, Shells Double Mixed Refrigerant (DMR) and Parallel Mixed Refrigerant (PMR), and the

Black and Veatch PRICO process. The optimal process for a specific project is dependent on many factors

including the feed stock composition, quantity of LNG to be produced and local ambient conditions. Each

process has different cycle efficiencies that trade off with varying levels of capital investment. A typical

refrigeration process map is shown in Figure 1. [Ed. note: All figures and Table 1 appear at the end of the

paper, beginning on page 7.]

All refrigeration cycles require compression equipment but the compression requirements for each process

vary as each cycle requires a different refrigerant gas (Propane, Ethane, Butane, Ethylene, Methane, and

Nitrogen). The resulting variation in gas properties leads to different compressor requirements but

compressor efficiency is critical to all process cycles as higher compressor efficiency has a direct impact on

improved LNG production for a fixed amount of power.

Since compressor performance has a significant impact on LNG production, it is industry practice to require

a shop test to verify the performance quoted is achieved. Standard industry guidelines (API-617 [1]) require

the test power to be within 4% of the quoted power. However, for LNG main refrigeration applications the

end user often requests the power tolerance be reduced to 2% to ensure the plant design production level isachieved.


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BACKGROUND

In 2007 the OEM initiated a multi-year effort to predict power within 2% while simultaneously extending the

operating range and efficiency of main refrigeration compressors. This effort required significant

improvements to the existing design process. Previous practice was to develop staging and then use one

dimensional (1D) tools to estimate the resulting performance. Two dimensional (2D) and three dimensional

(3D) or computational fluid dynamics (CFD) tools were used in the design process, but neither tool was

capable of predicting power consumption within 2%. Once a design was complete, a rig test was conducted

to validate the performance levels predicted by the 1D tool. The performance models in the 1D tool were

then empirically adjusted to match the test results. This process worked well if the stage under consideration

was within past design experience and a significant number of highly accurate rig test sets were available.

At the start of this effort a review was conducted of the entire design process (stage design, manufacturing,

and test evaluation) to identify areas for improvement. Based on the review it was determined that the

accuracy target could be achieved using previous practice if test rig accuracy was improved to 0.5% for

critical parameters (efficiency, pressure coefficient, flow coefficient). This solution path required significant

amounts of rig testing, especially to validate new designs as multiple iterations would likely be to achieve the

extended operating envelope required for the new designs.

The process evaluation included a cost tradeoff study to minimize overall program expense. This study

concluded that rig testing with a stage diameter much smaller (0.25-0.3m) than the production diameter (1.2-

2m) would reduce the overall cost and cycle time for the test program. While testing at a reduced size had a

cost benefit, it did create an additional prediction term in the performance prediction. Performance test

similitude is achieved for a given flow coefficient, tip Mach number, and volume reduction by direct scaling of

the production compressor geometry to a smaller size using a procedure described in ASME PTC-10 [3].

Unfortunately the Reynolds number is not preserved. The resulting test rig performance would, therefore, not

duplicate the performance of the production unit. This effect is commonly encountered with the OEM

compressor, but there were concerns that existing prediction models were not capable of achieving accuracy

requirement. It was determined that the only way to achieve the accuracy goal was to convincingly validatethe impact of scaling by quantifying the effect via rig tests at different sizes.

An alternate solution proposed was to improve the accuracy of the 3D CFD tools until they could achieve the

required prediction accuracy. This solution had two notable advantages. First, accurate CFD tools would

allow the designer to determine if new designs met performance goals prior to testing thus reducing the

number of required tests. Second accurate CFD tools could be used to predict the impact due to size,

eliminating the need to test at multiple sizes. However, the necessary improvements in the CFD tools

required accurate test results at multiple sizes for calibration. The drawback to this solution was that it was

unclear how much time it would take to achieve a reliable match between the CFD and test results.

It was ultimately decided to pursue both solutions in parallel as both solutions required accurate validation

data at various sizes to calibrate the impact due to scaling. By pursuing both options, progress toward the

ultimate continued, albeit at a slow pace, while work continued on the more challenging CFD prediction

improvements.

INVESTIGATIVE STUDY

The OEM maintains multiple rigs capable of testing different size impellers. For this study builds in the large

test rig were duplicated in the smaller test rig to benchmark the performance impact due to scaling. To

eliminate all other variables from consideration, all geometry was directly scaled with the scale factor defined

by the ratio of impeller exit diameter for the two tests (i.e., dsmall_rig/dlarge_rig). The directly scaled geometry

included all rotating and stationary components (inlet, inlet guide, impeller, diffuser, return channel, incomingsidestream and discharge volute). The direct scaling rules were also applied to secondary features including


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vane/blade features, thickness and machine fillets. The labyrinth seals were designed to maintain the

equivalent leakage area, thus the running clearance was directly scaled.

The large test rig is a large-frame, multi-stage centrifugal compressor, this test rig has been described

previously in the literature including, Gilarranz [4] and Sorokes et al [5]. This test rig has a pressure

containing case that was designed for maximum flexibility and allows different compressor arrangements to

be easily constructed. This enables testing of a variety of flowpaths, including sidestream configurations. Thetest rig has provisions to include moveable geometry in the stationary components at certain key locations

within the flowpath. The large rig is driven by a 22.4MW (30,000HP) steam turbine and speed reducing gear.

A typical machine configuration modeling a production propane compressor comprises 3-5 centrifugal stages

in a straight-through arrangement. A typical compressor arrangement and the location of the variable

geometry vanes are shown in Figure 2.

The aerodynamic flowpath can be heavily instrumented to maximize the amount of stage or components

parameters that are directly measured. Instrumentation that can be installed includes total pressure probes,

static pressure taps, dynamic pressure probes, total temperature probes, and 5-hole probes. Note that the 5-

hole probes measure static pressure, total pressure, and flow angle. The data from the 5-hole probes can

also be used to determine flow velocity at the probe location.

A typical schematic of the internal instrumentation layout used in each compressor stage is given in Figure 3.

The location of the instrumentation allowed measurement of the overall stage performance, as well as the

performance of each individual component in the stage. This allows the performance of the inlet guide, the

impeller, the diffuser and the return channel to be measured on an individual basis. The component data

measured during the testing was used for the validation and calibration of the 1D and 3D analytical methods

and tools used for stage design and performance prediction.

In addition to the large test rig, the OEM also has the capacity to test the same geometry in a small test rig,

which can be configured in either a single or two-stage arrangement. This particular test rig is capable of

testing impellers 0.3m to 0.5m (12-20) in size. The rig is driven by a 1.12MW (1500HP) electric motor and a

speed increasing gear, offering a wide range of operating speeds. A range of Mach numbers and Reynolds

numbers can be achieved by varying the test gas and suction pressure.

The rig is comprised of a series of stackable rings that form both the aerodynamic flow path and the rig

casing. The ring concept allows all instrumentation leads to be extracted thorough the outside diameter of

the rings, facilitating instrumentation connections to the data acquisition system. The stackable ring

construction allows greater flexibility in build configurations. It is possible to test a first stage configuration

(i.e., following a main inlet), an intermediate stage, a discharge stage (i.e., with a volute or collector) or two

stages with an intermediate sidestream. A typical schematic of the internal instrumentation layout used in

each compressor stage is given in Figure 4.

Both test vehicles are installed in a closed-circuit test loop and were run using R-134A as a test medium.

The testing was conducted in accordance with the ASME PTC-10 Code [3]. The test loop was also

instrumented in accordance to ASME PTC 10, with the intent of gathering flange to flange performance. A

schematic of the pipe loop instrumentation and measured parameters are shown in Figure 5.

The investigative study is based on several builds of the large test rig and the corresponding small test rig

builds. The selected builds were patterned after typical propane compressors using the AP-C3MR

process. The production compressor for this process typically contains 4 to 5 stages with incoming

sidestreams proceeding stages 2, 3 and 4. The impact of the flow entering through the sidestream has a

significant impact on the performance measured at the compressor flanges. The study outlined in this paper

focused on the impact of scaling and concentrated on the internal performance measured at the inlet and


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outlet of each stage. The impact of the incoming sidestream on performance has been documented in other

papers, Koch et al [6], Fakhri et al [7], and will not be discussed is this paper.

A typical build configuration of the large test rig and corresponding small rig builds is shown in Figure 6.

While the large test rig is patterned after a production compressor with up to 5 stages, the small test rig is

limited to 2 stages. Therefore, the small rig tests break down the domain of the large rig into representative

blocks of 1 to 2 stages for testing. In the example show in Figure 6 the first stage following the main inlet istested as a single stage with the tested domain stopping that the exit of the return channel. The remaining

stages are preceded by an incoming sidestream. In the small rig this was modeled by testing two stages in

series with a sidestream between the two stages. Only the data from the second impeller in the small rig is

used in this configuration, thus correctly simulating all operating conditions and geometry. For the last

impeller in the compressor the discharge volute was included.

Improvement of any prediction tool requires an accurate test measurement system and known geometry for

the tested equipment. Prior to testing, the data acquisition system was calibrated to provide a test

uncertainty of 0.5% for the measured flow, pressure coefficient, and efficiency (see Gilarranz [8, 9]). This

required a review of the data acquisition hardware and the calibration of pressure, temperature, and flow

instrumentation.

Uncertainty due to geometry variation was minimized through proper selection of manufacturing methods,

controlling part tolerances and verification through very detailed inspection. All impellers tested were single

piece machined (Figure 7). All hardware was inspected, with all blade and vane rows assessed using laser

scans to identify the true surface geometry.

COMPARISON OF TEST RESULTS

While many configurations were evaluated, this paper focuses on the results of two particular stages. The

basic geometric and performance parameters for these stages are shown in Table 1. The two selected

stages have a similar design machine Mach number and flow coefficient, but have different blading designsresulting in different performance characteristics. The Reynolds number is higher for the large test rig, due to

the larger passage widths. The existing 1D model predicted both the efficiency and the polytropic head

coefficient would increase from the small test rig to the large test rig. A small shift of the entire curve to

higher capacity was expected due to the thinner boundary layers which would allow the impeller to pass

increased flow at the same machine Mach number.

A comparison of the large rig and small rig results are shown in Figures 8 and 9. In these figures the

polytropic efficiency and pressure coefficient are plotted versus inlet flow coefficient. All values are

normalized by the design value to allow relative comparison of the results. The overall curve shape and

operating range are very similar between the large and small rig results as expected.

The results for stage 1 are shown in figure 8. At the design flow the pressure coefficient is slightly lower and

the efficiency is slightly greater than for the large rig compared to the small rig. The maximum capacity

increased and stability increased for the large rig compared with the small rig. The detailed inspection for the

stage 1 impeller indicated the impeller surfaces were within tolerance but at the upper limit and thus had

more material remaining than required resulting in approximately 0.5% smaller passage area and could

explain the reduced head at design. The results for stage 2 are shown in Figure 9. For stage 2 both the

pressure coefficient and efficiency improved for the large rig compared to the small rig. The maximum

capacity was unchanged.

The deviation between the test results and the existing 1D prediction model at the design flow rate are within

the 2% accuracy goal, but the existing model did not capture the differences in performance between the two

stages. While it is very difficult to quantify these small changes it was felt additional improvements could be

made to the existing model.


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ANALYTICAL INVESTIGATION

As discussed previously a parallel study was initiated to improve the accuracy of CFD-based predictions.

This project began with discussions with the CFD software vendor (ANSYS-CFX) and several

turbomachinery consultants in the U.S. and Europe who regularly used the software. Critical parameters that

could be sources of variation were identified in these discussions: the computation grid, the solver options

specified for each solution, the gas properties used by the software, the methods used to post-process the

results and compare with the tested results, and the accuracy of the test geometry and results geometry.

The team then undertook a systematic study to identify the sensitivity of the each of the critical parameters

and evaluate which combination of parameters best matched all available data. This required an extensive

amount of CFD analyses to evaluate the many different combinations. The validation exercise culminated in

a standard process that is now used by the OEM CFD analysts to predict performance. The standard work

document includes criteria for grid size and quality, selection of CFD solver options, gas properties, and

methodology for comparing CFD and measured test results, (see Kowalski et al [10]).

Comparisons of the CFD predictions for the tested geometry discussed previously are shown in Figures 10

and 11. The shapes of the CFD predictions were very similar to the tested results shown in figures 8 and 9.For the first stage the CFD predicted pressure coefficient and efficiency were greater respectively for the

large rig than the small rig. The overall compressor range was essentially unchanged. For stage 2 the

pressure coefficient and efficiency also improved. The maximum capacity for stage 2 increased a small

amount for the large rig compared with the small rig.

The tested deviation between the large rig and small rig performance at the design point is very similar to the

deviations from the CFD results. This good correlation between CFD and test was achieved without

empirical tuning which provides confidence the 3D tools can be used to estimate the impact of scaling for

new designs that fall outside the correlated range of the existing model. The slight over prediction of the

pressure coefficient and capacity for stage 2 while quite good might still be improved via additional

investigations.

CONCLUSIONS

This study demonstrated that the performance impact due to scaling can be quantified by testing the

compressor in both large and small sizes. The test results validate that while the scaling effects are relatively

small for these stages, they must be addressed to consistently achieve the desired prediction accuracy of

2% at the compressor design point. The results also indicate that one can have high confidence in the stage

performance prediction once reduced size testing is completed, thus eliminating the need for large rig

testing. Finally, the study has shown that CFD prediction has improved significantly and can now be used to

estimate the impact due to scaling when empirically correlated 1D tools are not available or outside the

calibrated range.

ACKNOWLEDGEMENTS

The author would like to thank Dresser-Rand Company for funding this overall project and for allowing the

publication of this work.

NOMENCLATURE

= flow coefficient =

Q = volumetric flow in cubic feet per minuteN = operating speed in rotations per minute (rpm)

D2= impeller exit diameter in inches

Machine Mach number =


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22bU

A0= sonic velocity of gas in meters per second (feet per second)U2= impeller tip speed in meters per second (feet per second)

Reynolds number =

= density in kg per cubic meter (pounds per cubic feet)

b2= impeller tip width in meters (feet) = viscosity in kg per meter per second( pounds per feet per second)

REFERENCES

1. American Petroleum Institute, 2009, API STD 617, Axial and Centrifugal Compressors and Expander-compressors for Petroleum, Chemical and Gas Industry Services, Seventh Edition.

2. Schultz, J. M., 1962, The Polytropic Analysis of Centrifugal Compressors, ASME Journal ofEngineering for Power, Vol. 84, pp.69-82, New York

3. ASME, 1997, PTC 10, Performance Test Code on Compressors and Exhausters, ASME Press.

4. Gilarranz, J., Actuation and Control of a Movable Geometry System for a Large Frame-Size, Multi-StageCentrifugal Compressor Test Rig, ASME Paper GT2007-27592, Proceedings of GT2007, ASME TurboExpo 2007, Montreal, Canada

5. Sorokes, J.M., Soulas, T.A., Koch, J.M., Gilarranz, J.L., 2009, Full-Scale Aerodynamic andRotordynamic Testing for Large Centrifugal Compressors, Turbomachinery Symposium Proceedings,Houston, USA

6. Koch, J., Sorokes, J., Belhassan, M., 2011,Modeling and Prediction of Sidestream Inlet Pressure forMultistage Centrifugal Compressors , Turbomachinery Symposium Proceedings, Texas A&M

7. Fakhri, S., Pacheco, J., Koch, J., 2012,Centrifugal Compressor Sidestream Sectional PerformancePrediction Methodology, Turbomachinery Symposium Proceedings, Texas A&M

8. Gilarranz, J. L., 2005, Uncertainty Analysis of a Polytropic Compression Process and Application toCentrifugal Compressor Performance Testing, Paper GT-2005-68381, Proceedings of GT2005, ASMETurbo Expo 2005, Reno, USA

9. Gilarranz, J. L., 2006, Uncertainty Analysis of Centrifugal Compressor Aero-Performance Test Data:Effects of Correlated Systematic Error Paper GT-2005-68381, Proceedings of GT2006, ASME TurboExpo 2006, Barcelona, Spain

10. Kowalski, S., Fakhri, S., Pacheco, J., Sorokes, J., 2012, Centrifugal Stage Performance Prediction andValidation for High Mach Number Applications, Turbomachinery Symposium Proceedings, Houston,USA


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Figure 1 -- AP- C3MRTM

LNG Process

Figure 2 Large Test Rig


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Figure 3 Typical Instrumentation for Large Test Rig

Figure 4 Small Test Rig


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Figure 5 Schematic of Typical Closed Loop Test Set-up

Figure 6 Typical Cross Section of Large Test Rig and Corresponding Small Rig Configurations

Table 1 Comparison of Key Parameters for Test Rigs

SpeedCompressor

InletDischarge

Test Gas Cooler

Flowmeter (Orifice)

Throttle

Valve

Cooling Water

P

PS

,TS

PT

TTPTTT

Pipe ID,

Orifice D

Test GasComposition

Stage #Inlet Flow

Coefficient

Machine

Mach Number

Impeller

Diameter

Reynolds

Number

Impeller

Diameter

Reynolds

Number

1 0.0969 1.131 47.335 6776301 12.385 2630000

2 0.1072 1.139 49.501 15442890 12.952 5630000

Large Rig Small Rig

Stage 1Followin main inlet

Stage 2 & 3Stage 2 - Following main inlet

Stage 3 - Following sidestream

Stage 3 & 4Stage 3 - Following main inlet

Stage 4 - Following sidestream


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Large Rig Impellers

Small Rig Impellers

Figure 7 Single Piece Machined Rig impellers


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Figure 8 Test results for Large Rig vs. Small Rig Stage 1

Figure 9 Test results for Large Rig vs. Small Rig Stage 2


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Figure 10 CFD Prediction for Large Rig vs. Small Rig Stage 1

Figure 11 CFD Prediction for Large Rig vs. Small Rig Stage 2

geometric scaling

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