Thermoacoustic Air Source Heat Pump Water Heaters: Design and Analysis

Introduction to Thermoacoustic Heat Pumps

Thermoacoustic air-to-water air source heat pumps (TAWASHPs) are emerging as an eco-friendly, simple, and cost-effective alternative to the existing compressor-based heat pump systems. Unlike traditional vapor compression refrigeration (VCR) systems, TAWASHPs utilize the principles of linear thermoacoustics to pump heat from ambient air to water without the need for a mechanical compressor.

The key advantages of TAWASHPs include:

Simplicity: TAWASHPs have a straightforward design with no moving parts like the compressor in VCR systems. They use a vibrating diaphragm of a loudspeaker as the means of work input.
Eco-Friendliness: TAWASHPs employ eco-friendly refrigerants such as helium, hydrogen, air, and nitrogen instead of synthetic refrigerants used in VCR systems.
Maintenance-Free Operation: The absence of a compressor makes TAWASHPs more compact and maintenance-free compared to VCR systems.
Precise Temperature Control: TAWASHPs can operate at lower frequencies (as low as 50 Hz) and maintain better coefficient of performance (COP) even at lower temperatures, unlike VCR systems that operate between 1200-4500 rpm and have reduced COP at lower temperatures.

In a TAWASHP system, the cold heat exchanger is exposed to ambient air, absorbing heat, which is then pumped to the hot heat exchanger by the thermoacoustic core (TAC). The hot heat exchanger transfers this heat to water, which can be used for various thermal applications such as space heating, hot water supply in hostels, community apartments, and hotels.

Design Optimization of the Thermoacoustic Core

The design optimization of the 1-kW TAWASHP system with helium as the working fluid is discussed in this article. The focus is on maintaining the hot heat exchanger temperature at 45°C and 55°C while subjecting the ambient heat exchanger to four different temperatures: -15°C, 0°C, 15°C, and 30°C, representing various atmospheric conditions throughout the year.

The key components of the TAWASHP system include:

Loudspeaker: Provides the acoustic work input to drive the system.
Thermoacoustic Core (TAC): Comprises the stack, ambient heat exchanger, and hot heat exchanger.
Resonator Tube: Encloses the TAC and is filled with helium gas.

The design methodology is based on Rott’s linear thermoacoustic theory, with the following considerations:

Parallel Plate Geometry: The stack, ambient, and hot heat exchangers are designed with parallel plate geometry for better performance compared to other geometries like spiral, circular, pin array, and honeycomb.
Materials: The stack is made of Mylar, and the heat exchangers are made of copper.
Operating Parameters: The average gas pressure is 10 bar, and the acoustic peak pressure amplitude is 0.3 bar, resonating at a frequency of 400 Hz.

The design process involves determining the critical temperature, normalized temperature gradient, normalized cooling power, and normalized acoustic power to optimize the performance of the TAC. The key design parameters, such as the stack center position, stack length, and heat exchanger lengths, are optimized to achieve the desired 1-kW cooling capacity while maximizing the COP.

Vertical Taper-Divergent Resonator Design

To avoid natural convection-driven heat transfer from the hot to the cold heat exchanger, the TAWASHP system is designed with a vertical taper-divergent and hemispherical (TDH) resonator. The vertical orientation ensures that the stack is placed above the ambient heat exchanger, and the hot heat exchanger is positioned on top, preventing the reverse transfer of heat.

The TDH resonator design includes the following features:

Loudspeaker with Helium Gas Spring: The loudspeaker is mounted on top of the vertical resonator and is equipped with a helium gas spring system to improve its electroacoustic efficiency from 3% to up to 52%.
Taper-Divergent Geometry: The resonator has a tapered section, a divergent cone section, and a hemispherical end, which are designed to minimize acoustic losses.
Quarter-Wavelength Configuration: The total length of the resonator is designed to be a quarter-wavelength of the oscillating helium gas, as this configuration has lower resonator losses and a more compact design compared to half or one-third wavelength designs.

The acoustic power dissipation in various sections of the resonator, including the ducts, taper, divergent cone, and hemisphere, is calculated using Rott’s equations. The total acoustic power dissipation in the resonator, stack, ambient heat exchanger, and hot heat exchanger is then determined to evaluate the overall system performance.

Validation with DeltaEC Software

The theoretical design and optimization of the 1-kW TAWASHP system are validated using the “Design Environment for Low-Amplitude Thermoacoustic Energy Conversion” (DeltaEC) software. DeltaEC is a one-dimensional software tool specifically designed to model and analyze the linear behavior of thermoacoustic devices.

The DeltaEC model is created by incorporating the various components of the TAWASHP system, including the loudspeaker, ducts, hot heat exchanger, stack, ambient heat exchanger, taper, divergent cone, and hemisphere. The guesses and targets are set to match the design requirements, and the model is iteratively adjusted to achieve the desired performance.

The DeltaEC results show that the TAWASHP system can deliver 1.55 to 3.35 kW of heat to the water, which is equivalent to 37.3 to 80.3 kWh of heat energy per day. The theoretical and DeltaEC results are in good agreement, validating the design optimization approach.

Practical Applications and Performance Analysis

The designed TAWASHP system can provide hot water at 45°C and 55°C for various thermal applications, such as space heating and domestic hot water supply. The performance of the system is analyzed in terms of the following key parameters:

Heat Rejection Rate: The heat rejected by the hot heat exchanger ranges from 37.3 to 80.3 kWh per day, depending on the ambient and hot heat exchanger temperatures.
Water Temperature Difference: The theoretical simulation shows that the TAWASHP system can heat a specific quantity of water by up to 86°C, depending on the mass of water and heating duration.
Coefficient of Performance (COP): The COP of the refrigerator (COPr) and the heat pump (COPh) are calculated, ranging from 1.1 to 2.34 and 1.58 to 4.75, respectively. The COP is inversely proportional to the temperature difference across the hot and ambient heat exchangers.

The results demonstrate the potential of TAWASHPs to replace the existing VCR-based air source heat pumps, especially for hot water applications in hostels, hotels, and other community spaces. The eco-friendly, simple, and maintenance-free design of TAWASHPs, coupled with their ability to deliver significant amounts of hot water, makes them a promising alternative in the future.

Conclusion

This article has presented the design optimization and analysis of a 1-kW thermoacoustic air source heat pump water heater (TAWASHP) system. The key highlights include:

Optimization of the thermoacoustic core (TAC) to maintain hot heat exchanger temperatures of 45°C and 55°C while considering various ambient conditions.
Design of a vertical taper-divergent and hemispherical (TDH) resonator to prevent natural convection-driven heat transfer and improve system performance.
Validation of the theoretical results using the DeltaEC software, which predicts the TAWASHP system can supply 37.3 to 80.3 kWh of heat energy per day to water.
Analysis of the practical applications, including the heat rejection rate, water temperature difference, and coefficient of performance.

The findings demonstrate the potential of TAWASHPs as a viable alternative to traditional VCR-based air source heat pumps, offering eco-friendly, simple, and maintenance-free operation for hot water applications in various settings. As the technology matures, TAWASHPs can become a promising solution for sustainable heating and cooling in the future.

For more information on air-cooled heat exchangers and their applications, please visit www.aircooledheatexchangers.net.