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“A one-dimensional model of a closed-loop refrigeration test block for centrifugal compressors”

Introduction

 

The increasingly competitive building equipment and control industry pushes manufacturers to devote more resources each year to research and development, continually improving the performance and efficiency of their products to develop and maintain a competitive edge. The design of centrifugal compressors is no exception to this trend, since these compressors are used in many power-intensive applications, including water-cooled chillers in large commercial and industrial buildings. The compressor transfers energy from the source (often a shaft driven by an electric motor) into the refrigeration cycle, and is thus a scrutinized component of the overall design.

Compressor development is an expensive endeavor because of prototyping and testing costs. The design of a new compressor requires at least one prototype to be constructed, which is then subjected to a series of industry-standard performance tests to quantify the improvements in the new design. This adds cost and development time to an already expensive process. For example, the costs for one week of testing can approach $10 000 (Sommer, 2013). The requirement of physical performance tests should not be disputed, since the resulting ratings are used by potential customers to compare offerings from different manufacturers. Additionally, all models are approximations of the real system and cannot completely capture the behavior of the physical system.

Nevertheless, minimizing testing time has a large impact on costs and time to market. A test block model based on first principles has the potential to reduce the testing time and thus decrease costs by assisting the test engineer in defining an optimized test plan built around test block capabilities at the expected ambient conditions. Furthermore, the downtime for changing flow measurement orifices can be minimized by providing a means to choose the best orifice diameter for a given range of test flow rates.

With these considerations in mind, the overall goal of this research is to create a thermodynamic model to simulate the 1500 hp gas block compressor testing equipment used by Johnson Controls, Inc. (JCI) at their facility in York, Pennsylvania. This equipment uses a hot gas bypass (HGBP) cycle to simulate the compressor operating conditions of the actual refrigeration cycle without requiring an evaporator or associated cooling load. The primary refrigerant used in this system is R-134a, but the equipment allows for a wide variety of refrigerants to be used, as should the thermodynamic model.

The model will use the design conditions of the new compressor (mass flow, pressure head, shaft speed, and isentropic/map efficiency) to determine the test block setup (flow measurement orifice size and cooling tower fan speed) required to conduct tests at given ambient conditions. The current testing process requires some trial and error to find a suitable test block setup for a new compressor. The thermodynamic model aims to quickly provide reasonably accurate initial estimates of the orifice diameter (based on differential pressure) and cooling tower fan speed (based on condenser heat transfer) required to test a new compressor at specified outdoor air conditions (temperature, barometric pressure, and relative humidity). Therefore, the testing time is reduced by eliminating (or at least minimizing) the trial and error phase of the testing process.

The equipment and configuration of a typical hot gas bypass test block cycle is described thoroughly in existing literature, primarily in work by McGovern (1984), Dirlea, Hannay, and Lebrun (1996), and Sahs and Mould (1956). Thermodynamic models of the individual components in the test block cycle exist, are well-established, and are used frequently in the thermal and fluid sciences. The novelty of this thesis is not derived from breakthroughs in the modeling theory surrounding the components, but rather from an integration of existing models into a holistic tool at an appropriate level for use in industry applications. Its significance may be measured by the impact on the daily workflow of test engineers in the compressor development group.

 

Figure 1.1: Comparison of idealized temperature-entropy (T-s) diagrams.

 

1.1 Background

A preferred method of evaluating compressor performance is to test the compressor on a closed-loop gas test block using the design process fluid (refrigerant) at design flow conditions. While the equipment can be expensive to construct, operate, and maintain, the gas test block makes isolating the compression portion of the refrigeration cycle easier. The basic premise of the gas test block cycle is that the cycle can maintain conditions at the compressor inlet similar to those experienced in a traditional vapor-compression refrigeration cycle, while the conditions at other points in the cycle need not follow the traditional refrigeration cycle arrangement. Temperature-entropy (T-s) diagrams for the typical vapor-compression refrigeration cycle and an idealized gas block test cycle are shown in Fig. 1.1, with process 1–2 representing the ideal, isentropic compression process for both cycles.

There are energy savings associated with using the gas test block instead of the chiller refrigeration cycle. Process 4–1 of the traditional refrigeration cycle of Fig. 1.1(a) is the result of heat transfer into the evaporator, which is the building cooling load or refrigeration effect. In a chiller test block situation, this load is simulated by mixing water from the condenser and evaporator loops. In the gas block test cycle, no water loop is required for this process, state 1 being reestablished instead by mixing saturated liquid-vapor mixture (state 6) with a superheated vapor separated from the discharge stream and throttled to the cycle’s low pressure (state 8). The conditions at state 1 are controlled by adjusting the discharge flow split that occurs near state 2 of Fig. 1.1(b). In addition to eliminating one water loop from the system, the condenser heat transfer—process 4–5 of Fig. 1.1(b)—is also reduced because only a portion of the refrigerant flow must be condensed.

A primary benefit of this arrangement is that the gas block is more versatile than a traditional refrigeration cycle used in a chiller. The gas block can handle a wide variety of test gases (refrigerants) and their associated operating pressures and cooling loads, while a chiller may require different heat exchangers or piping to operate with certain refrigerants at a full range of operating conditions. Additionally, the gas test block provides better locations for instrumentation and conforms to industry-standard test codes (for example, ASME PTC 10) outlining proven and well-established data analysis and results reporting methods. For example, the test code specifies straight sections of suction pipe and/or flow straighteners to produce near-axial flow, while the compact piping arrangement on a chiller causes large deviations from axial flow. Using a gas test block provides an even basis of comparison for compressors independent of the chiller design. A simplified schematic of the test block layout is shown in Fig. 1.2, with state numbering corresponding to Fig. 1.1(b).

1.2 Motivation

As discussed in the opening of Chapter 1, the numerical model of the test block will reduce the time required during physical testing of new compressor designs by helping engineers choose an appropriate test setup for a particular compressor. The parameters of the test setup predicted by the model include the flow measurement orifice diameter and the cooling tower fan speeds.

Additionally, the model will check whether or not a set of test conditions can be achieved at specified outdoor air conditions. These air conditions limit the performance of the cooling towers and may preclude certain compressor tests. This prediction could prevent the loss of time and resources required to set up a compressor test for conditions that are not feasible at the current outside temperature and humidity.

 

Figure 1.2: Simplified schematic of the 1500 hp gas test block facility.

 

Finally, JCI has expressed interest in building an automated test block in the future. If desired, the present model could be adapted for use in a model-based controls design workflow to expedite and enhance the control system design process. This is a long-term motivation and is secondary to the test time reduction and limiting conditions motivations.

1.3 Objectives

The overall goal of this research is to develop a one-dimensional, steady-flow thermodynamic model representing the 1500 hp gas test block at JCI’s York, PA facility. The numerical model will be used in conjunction with compressor maps and/or computational fluid dynamics (CFD) models of the compressors to quantitatively predict the performance of new compressor designs on the test block. To accomplish the overall goal and satisfy the needs of JCI (Iancu, 2012), the model must

  • compute the power requirements for the prime mover of the test block,
  • choose the orifice diameter that results in the smallest error in measured flow rate over the desired range of operating conditions, and
  • report the limits of the test block operating conditions for a given compressor design, test block control settings, and ambient air conditions.

1.4 Requirements and Constraints

The compressor test block model should be one-dimensional and steady-flow in nature; that is, the flow conditions at a cross section of flow are treated as spatially uniform and constant over time. Modeling is conducted on a macroscopic level, neglecting the effects of property gradients within the flow, such as viscous and thermal boundary layers. Modeling such detailed phenomena would complicate the model and would not significantly improve the predictions requested by JCI listed in Section 1.3.

The numerical model must be easy for engineers in the compressor engineering group at JCI to use and update and should minimize dependencies on licensed software for better portability. The software tools generally available to the compressor engineering group are Engineering Equation Solver (EES) and Matlab/Simulink. Engineering Equation Solver was chosen since Matlab/Simulink is more suited to dynamic models, the engineers at York are more familiar with EES, and EES has built-in thermophysical property relations while Matlab/Simulink requires interfacing with an external library.

The execution time of the model is a primary concern of JCI’s compressor engineers, and should be less than one minute for each individual compressor test. The accuracy of the model is another critical requirement. Output variables concerning the compressor and flow measurement orifice must not deviate from experimental results by more than 5%. At other areas in the cycle, such as at the condenser and cooling tower, a relaxed maximum deviation of 10% is required. This is justified by the inherent complexities in modeling the heat transfer in both the condenser and cooling tower and the relatively small impact on the desired outputs.

1.5 Organization

This thesis documents the creation of the one-dimensional, steady-flow test block model for use by compressor development and test engineers at JCI’s York, PA location. Chapter 1 has introduced the work, its motivation and objectives, and provided an overview of the assumptions and form of the project. Chapter 2 summarizes the current state of the art compressor testing and modeling techniques and other reference materials used in developing and implementing the model. Chapter 3 presents the mathematical formulation of the model and its inherent engineering assumptions. Chapter 4 documents the implementation of the numerical model, including numerical solution techniques and user interface considerations.

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Chapter 5 presents the predictions of the model for a variety of compressor designs and operating points. These predictions are compared to corresponding experimental data from physical tests to validate the model predictions. A discussion of the validation results is included, highlighting the strengths and weaknesses of the numerical model. Chapter 6 summarizes the research work and provides recommendations to users of the model and future maintainers.

Appendix A contains code listings of the EES implementation for the compressor gas test block model described in Chapter 4. Brief explanations of the code are included. Appendix B presents a sample set of validation results. This includes a set of experimental data from the test block data analysis program and the corresponding model outputs. The validation effort is described in detail in Chapter 5.

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