A Thermoacoustic Device for Heat Recovery

Design of a thermoacoustic heat engine for low temperature waste heat recovery in food manufacturing

(A thermoacoustic device for heat recovery)

J-A. Mumith, C. Makatsoris*, T.G.Karayiannis

School of Engineering and Design, Brunel University, London, U.K.

* Corresponding Author. Tel.:+44 (0)1895 265063

E-mail address: , ,

ABSTRACT

There is currently an urgent demand to reuse waste heat from industrial processes with approaches that require minimal investment and low cost of ownership. Thermoacoustic heat engines (TAHE) are a kind of prime mover thatconvert thermal energy to acoustic energy, consisting of two heat exchangers and a stack of parallel plates, all enclosed in a cylindrical casing. This simple design and the absence of any moving mechanical parts make such devices suitable for a variety of heat recovery applications in industry. In this present work the application of a standing-wave TAHEto utilise waste heat from baking ovens in biscuit manufacturing is investigated. An iterative design methodology is employed to determine the design parameter values of the devicethat not only maximiseacoustic power output and ultimately overall efficiency,but also utilise as much of the high volume waste heat as possible. At the core of the methodology employed is DeltaEC, a simulation software which calculates performance of thermoacoustic equipment. Our investigation has shown that even at such a comparatively low temperature of 150 it is possible to recover waste heat to deliver an output of 1,029.10W of acoustic power with a thermal engine efficiency of 5.42%.

Keywords:Thermoacoustic heat engines; Heat recovery technology; Food Manufacturing; Simulation

1. Introduction

In recent years there has been a renewed interest in heat recovery technologies for the utilisation of waste heat from industrial processes. This is due to new legislation, the urgent need to reduce dependency on fossil fuels and concerns of the negative impact of many dated and unsustainable industrial processes on the environment. In particular, in biscuit manufacturing the biscuit dough is heated during baking at elevated temperatures in gas fired ovens. As a result of this baking process, exhaust gas is expelled from the baking oven and released into the atmosphere via an exhaust gas flue.

In this paper, for the first time an investigation and assessment of the potential of thermoacoustic heat engines to a real-life industrial process is presented. The aim of the investigation is the utilisation of high volume flow rate but low temperature waste heat dischargedfrom the baking process in high volume biscuit manufacturing. Typically, applications of thermoacoustic heat engines are for low power levels, so far limited to a maximum of 6kW thermal power input [1]. The application of this technology in food manufacturing is very attractive due to the low investment requirements and low cost of ownership. This is because overall designs are very simple as they require no moving parts, exotic materials, close tolerances or critical dimensions [2]. Furthermore, they are small geometrically, therefore unlike other heat recovery technologies based for example on the Organic Rankine or the Kalina cycle [3], TAHEs do not have significant ‘footprint’[2].Also, compared to conventional heat recovery approaches, this technology can be used in a variety of applications because energy can be converted into a more useful form.

1.1.Overview of thermoacoustic heat engine technology

Thermoacoustic heat engines have the following four essential elements, fig. 1:

1. high temperature heat exchanger (High T HX),
2. stack,
3. ambient temperature heat exchanger (Ambient T HX),
4. resonator.

The thermoacoustic heat enginein Fig.1 consists of two heat exchangers. Those are the engine’s heat source and heat sink, a stack where input thermal power is converted to acoustic power (a form of mechanical power), and a resonator which is a cylindrical tube encompassing all components and is the solid container for the acoustic wave generated.

The key mechanism for energy conversion from thermal to acousticis the thermoacoustic effect, occurring in the TAHE when certain conditions aresatisfied. A compressible fluidis used as the working fluid within the engine, which in most cases is an inert gas such as helium.Acoustic waves occur naturally as a result of a temperature gradient across the stack as heat transfer occurs between the compressible fluid and a solid boundary (stack).The transfer of thermal energy to and from the compressible fluid and the stack creates local changes of pressure and velocity in the working fluid. When there is the correct pressure-velocity phasing, acoustic oscillations appear spontaneously creating an acoustic wave. Depending on the pressure-velocity phasing either a standing-wave or a traveling-wave is created. A standing-wave pressure-velocity phasing is shown Fig.2. The pressure the acoustic wave generates creates mechanical work, which can then be easily recovered to generate for example electric power. In this work a standing-wave thermoacoustic heat engine is evaluated due to its simple design, as can be seen in Fig.1.

The field of thermoacoustics is an emerging one, with its primary focus on a deeper understanding in an effort to increase the performance of the engine [2,4-7]. A recent development in the field of thermoacoustics is research that demonstrates the various ways in which TAHEs can be used in order to realise practical applications including refrigeration, lifting temperature of a heat source and generating electricity [8-11]. One example of such work is the utilisation of waste heat from an internal combustion engine to drive a thermoacoustic refrigeration system for automotive applications. In this particular instance the TAHE only harvests 6kW from a total of 145kW of thermal power that is rejected from the internal combustion engine[1]. Another example is the work carried out regarding a thermoacoustic heat pump for upgrading industrial waste heat to a higher temperature by the Energy Research Centre in Netherlands, again only limited to a maximum thermal power input of 5 kW [9], whereas this work looks at the effects of relatively high power levels on the design of a TAHE in order to utilise high volume, low temperature waste heat. Also, attempts have been made in recent years to design efficient thermoacoustic electricity generators, where the acoustic power produced in the thermoacoustic engine is converted to electric power by coupling the engine with a type of transducer; these have achievedacoustic-to-electric conversion efficiencies of up to 77%[12-14].

The aim of the paper is to investigate and assess the application of this technology to the biscuit baking process in a large biscuit manufacturer. As the food manufacturing process results in waste heat that is comparatively low temperature and high volume, the thermoacoustic heat engine must be carefully designed to maximise performance of the device as well as maximising the utilisation of the waste heat. Various parameters ranging from materials to the geometry of the engine are considered during the design process in order to meet the criterion mentioned.

In the following section the design parameters, iterative methodology and simulation model are outlined and discussed. Then in section 3, the results are presented and analysed. Finally the main conclusions as well as limitations and further work are discussed.

1. Thermoacoustic heat engine for biscuit baking

The rejected gas mixture from the baking oven comprises CO2, N2, O2 and H2O,at a temperatureof approximately 150,a volume flow rate of 1,288, and the corresponding density of the exhaust gases is 0.797kg/m3. Therefore, the waste heat is calculated as depending on the outdoor air temperature which varies over the course of the year.For the mean annual temperature in England of [15], is 40.35 kW from a single exhaust gas flue.

The thermoacoustic heat engine is to be installed in the exhaust gas flue, perpendicular to the flow of the exhaust gas so that heat can be transferred to the working fluid through the high temperature heat exchanger (High T HXsection in Fig.1). The material and geometric properties of the TAHE will be varied in order to maximise the performance of the engine and utilise as much of the waste heat as possible.

1. Thermoacoustic heat engine design

2

3

3.1Design parameters

There are two important parameters in thermoacoustics; the total thermal power that is available for conversionin the TAHE and the acoustic power, which is the useful mechanical work that is produced in the stack.

/ (1)

whereRe[] denotes the real part of the terms inside the bracket, and the tilde denotes the complex conjugate.

The energy available for conversion is related to the energy of a flowing fluid, and hence enthalpy is given by Eq.(1). The second term in Eq.(1), is the thermal conduction that occurs in the working fluid and solid plate of the stack, causing losses of energy as this energy does not contribute to the thermoacoustic effect and hence it is taken away from the energy available for conversion.

Acoustic power generated in a thermoacoustic heat engine is related to the work done by a differential volume of fluid in the stack section, as it expands from to, and so the work is.The time-averaged acoustic power is the product of and that is produced near the surface of the stack plate,

/ (2)

From these two equations that can be found in [2] and previous experimental work [2,16-18], 12of the most significant design parameters are identified and considered in this work for the design of the TAHE for low temperature waste heat recovery, see Table 1. Also the thermal power input is another design parameter of the engine, in order to observe the behaviour of the TAHE and how performance is affected with relatively large thermal power levels.

Higher mean pressure and drive ratio DR, which is the ratio of peak pressure amplitude to the mean pressure,yield greater power density. However,higher valuesfor these two design parameters lead to an increase in the viscous penetration depth, the region in which power is dissipateddue to viscosityand there is a greater risk of nonlinear effects (i.e. turbulence) occurring which diminish the performance of the engine. This suggests that there is an optimum mean pressure and drive ratio that provide good power density and do not significantly affect the thermal penetration depth(the region in which heat from the solid plate diffuses into the fluid and acoustic power is produced). It is also necessary to consider the maximum mean pressure that reasonable fabrication methods can accommodate with regard to the resonator see Fig.1. Therefore, the range of mean pressure value that is employed in the iterative process is 1MPa-3MPa [19,20], based on values used in previous experimental work. The drive ratio is calculated by the simulator as a result of the thermal power input specified.

Normal heat exchanger calculation methods cannot be used to determine the thermal power extracted from the exhaust gas, as the volume flow rate in the TAHE is oscillatory and hence the time-averaged flow is zero. Furthermore, the operating conditions which affect the thermal power input do not remain the sameand so the output temperature of the high temperature heat exchanger cannot be determined. Thus a wide range of was adopted,to observe how the TAHE behaves at these larger power levels and how various thermal power inputs affect the material and geometric parameter values that produce the greatest performance in the TAHE. A single TAHE will not be able to handle a large thermal power input as the very large pressure amplitudes created would cause nonlinear affects accounting for significant losses and degradation of performance [11]. Therefore a thermal power input of up to 19kW is considered in this work.But this limitation of the engine can be mitigated by using multiple TAHEs together.

The working fluid’s Prandtl numberPr() determines the fraction of the energy passing through the stack that will dissipate due to viscosity. Also, higher speed of sound yields greater acoustic power, as the time taken to create a standing-waveis reduced. In some cases a small fraction of lighter gases are mixed with a heavier gas in an effort to reduce the Prandtl number, but sacrificing power density, as the added mass reduces the speed of sound [24]. A mixture of Helium and a lighter gas Argon [25] was used for this work, varying the mole fraction of Argon from 0-100% to determine numerically from the iterative process how this directly affects the acoustic power output and acoustic losses of the system.

There are two aspects of the stack that have a direct effect on the acoustic power produced, the material and geometric properties. The thermophysical properties (,) of the stack should be such that heat capacity is as high as possible to enable heatto move along the stack in the x direction by the constant heat transfer between the stack and the working fluid, but have low thermal conductivity to minimise ordinary conduction of heat along the stack which causes dissipation of power [24]. Hence, stainless steel was used as it is readily available and its heat capacity is approximately 30 times more than its thermal conductivity.

The stack length plays a direct role in the desired performance of the engine as it is in the stack region that acoustic power is produced. It can be determined numerically from the temperature gradient, as it is above a critical temperature gradient that acoustic power is produced. Also care should be taken that the stack is located where is small to reduce viscous dissipation caused in the region of the viscous penetration depth, which prohibits the transfer of heat from the stack to the working fluid. This is a fundamental aspect of the thermoacoustic effect generating acoustic power. For this to take place, the stack position should be close to the pressure antinode of a standing-wave, see Fig. 2. But standing-wave systems produce acoustic power proportional to and at a particular location. Therefore, there is an optimum position in the engine where maximum acoustic power is produced and minimum losses occur, which is typically between and [21,22], therefore this range of values is used in our design methodology. The Blockage Ratio BR isdefined as the ratio of the cross-sectional area occupied by the gas to the total cross sectional area, and represents the extent to which the plates are tightly packed in the stack section[25]. It is a design parameter that is intended to take into account the effect of the stack on the acoustic field. Previous experimental work has shown that a value of 0.8 yields good results, and is therefore used in this work [2,6]. The plate spacing is a crucial parameter as it determines the strength of the interaction between the working fluid and the stack in terms of heat transfer and hence temperature of the working fluid. Typical values for the half plate spacing for a standing-wave thermoacoustic heat engine is between and 4[19,21,22]. In this work the half plate spacing is kept constant at.A gap which is any larger will weaken the interaction between the working fluid and stack and ultimately negatively affect the performance of the engine.This has been found to be the case when running simulations varying the half plate spacing between and 4.

3.2Iterative Design methodology

An iterative design process has been developed with whichan incremental change in a design parameter value is made within the range of values shown in Table 1. Each time a new value of a design parameter is set as the input,the simulation is run and the output values (thermal stack efficiency, thermal engine efficiency) are assessed according to the following criteria: maximum power in stack and; minimum acoustic losses in engineas shown in Fig.3. Also various design parameters are varied simultaneously during a simulation to observe the relationship to each other and ultimately how they affect the performance of the engine. At the core of this approach is DeltaEC, a simulation code developed by Ward et.al. [26] specifically for the design and assessment of thermoacoustic systems.

3.3Standing-wave model simulation

DeltaEC has been employed for analysis and simulation [26]. This is a simulation code that provides information regarding the performance of thermoacoustic equipment. It also aids the user to design equipment to achieve some desired performance. In this simulator, a thermoacoustic system is represented by a series of segments, such as duct, cone, stack, heat exchanger,and is modelled in steady state conditions. The wave equation employed in the simulator without viscous or thermal-hysteresis losses is,

/ (3)

This second-order equation can be reduced into a system of two first-order equations with respect to pressure and volume flow rate:

/ (4)
/ (5)

These are the most fundamental equations required to find the pressure and volume flow rate of the system as a function of x.Additionally the simulator takes into accountthe dissipation of acoustic power along the inner walls of the cylinder due to viscous effects. Different segments use different equations to account for local conditions. For example, the governing equations in large-diameter ducts and shallow cones are,

/ (6)
/ (7)

where and are the spatially averaged thermal and viscous functions, and is the plate heat capacity correction factor. If then the pressure gradient of Eq.(6) is completely inertial, but if then the existence of viscosity and stationary boundaries adds a resistive component to the pressure gradient and also effects the size of the inertial influence. The spatially averaged thermal function represents the thermal contact between the working fluid and solid plate,if then thermal contact is perfect and if there is no thermal contact between working fluid and solid plate [23].It is these equations that are used for the hot and ambient duct that is modelled in the simulator.