Energy-efficient Legionella control that mimics nature and an open-source computational model to aid system design

Highlights


Introduction
Use of energy efficient domestic hot water (DHW) systems has increased in recent years as energy costs and energy efficiency standards have increased. Water heating accounted for 18.7% of household energy usage for houses built in the United States between 1980 and 1989 and reduced to 17.8% for houses built between 2000 and 2009 [1] . The United States' energy efficient water heater market increased from 625,000 ENERGY STAR approved units sold in 2006 to 1 million sold in 2009 [2] , and the U.S. federal minimum standards for energy factors of hot water storages tanks just increased in 2015. In 2008, the European Union set the goal of reducing the energy requirements of new buildings by 20% by 2020, and the addition of solar DHW systems has been shown as one way to reach this goal [3] , and global use of solar hot water systems has been increasing. The annual global volume of solar water collectors increased from 1.8 kW th per 1000 inhabitants in 2000 to 12.0 kW th per 1000 inhabitants in 2012 [4] , and the annual capacity of solar thermal collectors in the EU28 countries and Switzerland nearly doubled from 2004 to 2013 [5] .
Cases of Legionnaire's disease, an acute form of bacterial pneumonia often caused by exposure to DHW systems with Legionella pneumophila infestations, have also been increasing. In the United States, the cases of Legionnaire's disease per 100,000 persons nearly tripled from 0.39 in 2000 to 1.15 in 2009 [6] . During that same time period in Europe, cases of Legionnaire's disease per 100,000 persons increased from 0.538 in 2000 to 1.10 in 2009 [7], [8] . Increases in the occurrence of Legionnaire's disease cannot be directly connected to trends of energy efficient and renewably powered DHW use. However, Legionella p. grows well in water maintained between 25-45 °C [9] and can survive temperatures of 66°C for several minutes [10] , and these temperatures are typical in energy-efficient and solar DHW systems. As an example, energy efficient DHW systems heated by air-source or ground-source heat pumps typically have operating temperatures of 50-55 °C [11] , which still permits Legionella growth. Although water temperatures within solar collectors can reach daily maximums of around 90 °C, storage tanks are typically maintained under 50 °C to minimize standby heat loss [12], [13] .
Many thermal, chemical, and irradiative methods for preventing and treating Legionella colonization in hot water distribution systems exist [14] , the most common including hyperchlorination, super-heat-and-flush, and maintain storage tanks above 55°C. All these methods have the downside of high cost; both thermal methods are energy-inefficient while hyperchlorination is potentially hazardous to the health of users [15] .
One potentially energy and cost efficient method is to thermally disinfect water immediately prior to exiting a hot water outlet. The general system design, shown in Figure 1, mimics countercurrent heat exchange present in the circulatory systems of many birds. Ducks, for example, have a structure of closely connected arteries and veins called rete in the legs and feet which act as a biological heat exchanger; warm arterial blood coming from the body donates heat to cold venal blood returning from the feet. This action reduces the energy input necessary to bring blood returning from the feet back to body temperature by a factor as large as 84 [16] . Thus, we refer to any design which transfers heat between fluid in a single continuous flow to aid a heating or cooling process a "duck foot" (DF) heat exchange system (see Figure 1). Such systems are ideal for the point-of-use eradication of Legionella or other pasteurization applications such as flow through solar water pasteurization. Figure 1. General design of a "duck-foot" heat exchange system. Fluid entering at temperature T 1 changes by ΔT in the heat exchanger to T 2 . After passing through some kind of reservoir, fluid re-enters the heat exchanger at a temperature very near T 2 (due to heat gains/losses to the environment). Fluid exits the heat exchanger at an output temperature near to the input temperature T 1 .
Black and White Print DF heat exchange systems are common design features in dairy pasteurization plants and flow through solar water pasteurization systems [17] . Other applications include processes during which fluids must increase in temperature before cooling. For example, the solar dairy pasteurization system presented by Quijera et al. (2011) and the solar honey pasteurizer presented by Evans and de Schiller (1997) would have improved their efficiencies by including DF heat exchange systems [18], [19] .
Many models exist for the design optimization of plate heat exchangers. McKillop and Dunkley (1960) first presented a thermal model for calculating fluid temperatures within the channels of plate heat exchangers using the Gill-Runge-Kutta method for solving the system of first order ordinary differential equations [20] . Gut and Pinto (2003) developed an assemblage algorithm for modeling generalized plate heat exchanger configurations which considers the temperature dependence of fluid properties within heat exchange channels and solved the system of first order ordinary differential equations using the computational software gPROMS [21] . Strelow (2000) presents a non-iterative method for modeling heat exchangers with multiple process streams and unusual geometries [22] . To the authors' knowledge, however, no models exist specifically describing DF heat exchange systems without manipulation. Additionally, existing plate heat exchanger models require knowledge of solving systems of first order differential equations and often additional, expensive computer software to run; thus, they are inaccessible to many potential users. The aim of this project was to develop a simple, easy-to-use model specific to DF heat exchange systems using widely available computer software. The model is intended to assist designers thinking of implementing DF heat exchange systems for Legionella spp. control or for a variety of pasteurization applications including solar water pasteurization. For a single-pass plate heat exchanger with N plates and N+1 channels, the DFHXM uses symmetry to approximate the system as two countercurrent fluid channels, each with half the total channel volume, and scales the result by N. The idealizations outlined by McKillop and Dunkley (1960) were used while making the model: (1) fluid properties are independent of temperature; thus, the overall heat transfer coefficient is constant within the heat exchanger, (2) no heat is lost by the fluid or heat exchanger material to the external environment, (3) no heat is conducted in the direction of fluid flow, and (4) temperatures and flow rates within control volumes in fluid channels are constant [20] . An additional assumption for DF systems is that mass flow rates are equal for both flow directions within the heat exchanger.

Model Description
The model breaks the two-channel approximation into n partitions along the direction of flow to create 2n fluid control volumes ( Figure 2); each fluid control volume represents the sum of channel volumes at a given partition level on each side of the heat exchanger. The time step is dependent on mass flow rate , the volume V cv of control volumes, and the fluid density (assumed constant) ρ as . The time step can be adjusted for a given fluid by changing the mass flow rate or the number of partitions n, which is related to control volume size by (see Table 1

Using the Duck Foot Heat Exchange Model
The DFHXM can be run in versions of Microsoft Excel 2007 and newer and is available without cost [23] . Users must input the parameters listed in  [24] . Increasing the number of partitions n improves model performance by decreasing the size of control volumes and the length of time steps, but calculation time also increases.   Table 2.

Constant Heater Outlet Temperature
Fluid passes the heater outlet at a constant temperature , which is a necessary input parameter. All parameters relating to the heating reservoir may be omitted.

Heating Reservoir without Thermostat
Fluid passes the heater outlet from a heating reservoir with volume , constant power , and initial temperature . All other heating reservoir parameters and may be omitted.

Heating Reservoir with Thermostat
Identical to Heating Reservoir without Thermostat with the addition of a thermostat maintaining reservoir temperature between and after initial warm-up or cool-down of the heating reservoir. The user may omit , , and .

Heating Reservoir Ramped Power
Identical to Heating Reservoir without Thermostat, but the heater begins with an initial power and ramps linearly at a rate to a final power . No maximum temperature is set for the reservoir, and the user may omit , , and .
The Constant Heater Outlet Temperature mode allows users to investigate the effects of heat exchange area and heat load on the transient and steady-state characteristics of a DF system by simulating a "limitless" heating reservoir. The Heating Reservoir without Thermostat mode allows users to investigate the effects of heating reservoir volume, power, and temperature on the transient and steady-state characteristics of a DF system, as well as differences in energy usage.
No upper limit is placed on reservoir temperature to ensure that equilibrium temperatures reflect the heat transfer capacity of the heat exchanger. The Heating Reservoir with Thermostat mode is the most realistic simulation of DF heat exchange system and includes a reservoir maximum temperature and hysteresis. The final mode, Heating Reservoir Ramped Power, was created to mimic DF systems with non-constant power sources such as wood or solar heating.

Model Validation
An experimental DF heat exchange system was built by Infjärdens Värme AB in Piteå, Sweden, in 2009 and is shown in Figure 3. Measurements were conducted at the Luleå University of Technology (LTU) as part of a Senior Design Project in Renewable Energy in 2013 [25] . The

Black and White Print
Water at a constant flow rate and temperature was run through the system prior to taking measurements, and temperatures were recorded each minute after power was supplied to the heating reservoir. Steady-state temperatures for each flow rate are listed in Table 3; however, it should be noted that flow rates varied up to 6% from reported averages during experimental trials. The DFHXM heater power was set to 2700 W to account for an estimated 10 % energy loss in the system, which is reasonable considering calculated power delivery from the experimental heater averaged 8.7 % lower than the rated level of 3000 W. Remaining thermal losses were assumed to occur through pipes and connections. The overall heat transfer coefficients used for simulations were calculated from experimental steady-state temperatures for each flow rate; parameters for simulation runs are also listed in Table 3. The number of partitions n was adjusted for different simulations to ensure nearly equal time steps of 0.11 s. Table 3. Experimental steady-state temperatures and DFHXM simulation parameters for the four investigated flow rates.
Measurement locations of T 1 , T 2 , T 3 , and T 4 are shown in Figure 3. The Heating Reservoir with Thermostat mode of the DFHXM was run for each experimental flow rate; although, steady-state temperatures in the reservoir were always below thermostat temperature, and the simulated thermostat never engaged. The DFHXM simulations agreed well with experimental results as shown in Figure 4 for both transient and steady-state temperatures.

Flow Rates
Excluding the results for inlet temperature T 1 which was an input parameter (T i ) for the DFHXM, the most inaccurate simulation was of the 3.8 kg min -1 trial. The average deviance from experimental steady-state temperatures for T 2   The Heating Reservoir with Thermostat mode of the DFHXM was used for every simulation, and parameters are listed in Table 3.
Experimental steady-state temperatures and DFHXM simulation parameters for the four investigated flow rates. Measurement locations of T1, T2, T3, and T4 are shown in Figure 3.. Temperature numbers (T x ) correspond to labels in Figure 3. The

Black and White Print
A drawback to using the DFHXM is the necessity to estimate heat losses to the external environment. Had the heating reservoir's rated power of 3000 W been used, the model would have overestimated steady-state temperatures by 9.3 % at 3.8 kg min -1 and as much as 2.1 % with the other flow rates. However, accounting for thermal losses by decreasing the simulated heater power, as was done in this simulation, gives users the freedom of investigating different levels of system efficiency.

Example Simulations
The DFHXM calculates the temperature profile along the heat exchanger and within the reservoir volume through time. Sample results from a simulation run of the Heating Reservoir without Thermostat mode with the input parameters in Table 4 are shown graphically in Figure 5 as transient temperature profiles in the heat exchanger ( Figure 5a) and heating reservoir (Figure 5b) as the system approaches steady-state. The chosen parameters are reasonable for a DF system installed for Legionella control with a single shower. After 10 seconds, water in the middle regions of the heat exchanger remained near the starting ambient temperature of 20 °C, while the reservoir was still near its starting temperature of 75 °C, being not much yet diluted by influx of cooler water. Water entering the heater inlet had already risen to nearly 50 °C due to heat received from water exiting the heating reservoir. After 30 seconds, ambient temperature water had been fully flushed from the system, but areas near the inlet and outlet still required more energy input to rise above the temperature of incoming water at 40 °C. The reservoir temperature further reduced due to thermal mixing of entering water. After 60 seconds, the system was nearly at equilibrium. The temperature profile along the heat exchanger was nearly linear, and temperature within the reservoir approached its horizontal asymptote.

Black and White Print
Because the intended purpose of DF heat exchange systems is for disinfection by pasteurization, the ability to monitor the temperature within the reservoir tank for different system arrangements is important for design. For example, imagine a system with the parameters listed in Table 4 equipped with a 10 kW heating reservoir and a thermostat set to a maximum temperature of 78 °C with a hysteresis of 6 °C. If the desired function is Legionella spp. eradication, the temperature of the reservoir should never drop below 70 °C to ensure no infected water exits the tap to create dangerous aerosols. Heating reservoir volume is an important design consideration to system function and energy consumption; with too small a tank the water temperature will sink below 70 °C due to thermal mixing of cooler water entering the tank, while standby energy loss increases with tank volume. The DFHXM was used to find an optimal tank volume to ensure safe function and minimize energy losses. Figure 6 shows the reservoir temperature versus time for different reservoir volumes. Thermostat simulation. Input parameters were identical to those in Table 4 except P was 10,000 W, maximum reservoir temperature was 78 °C, and hysteresis was 6 °C.

Black and White Print
Temperatures in larger reservoir volumes were less affected by thermal mixing of entering water than smaller volumes. Larger reservoirs also had longer cycling times of the heater, but this did not affect the energy usagethe heater was powered 77% of the time regardless of reservoir volume. Larger reservoir volumes, however, use more energy due to increased surface area and standby heat losses. In this scenario, a 26 L heating reservoir was ideal, minimizing standby heat losses while always maintaining the reservoir temperature above 70 °C.
Another potential application for the DFHXM is solar pasteurization system design. Imagine that a 25 L reservoir with a flow rate of 1.0 L min -1 receives linearly increasing power from 0 to 750 W per m 2 solar collector area over a span of 6 hours. Such a system could be used to disinfect drinking water, and designs could consist of solar collectors focusing energy upon the 25 L flow-through reservoir. The Heating Reservoir with Ramped Power mode of the DFHXM was used to simulate changing solar power and monitor temperatures in the heating reservoir through time.
The heat exchanger and fluid parameters were identical to those in Table 4 except that fluid flow rate was 0.0167 kg s -1 and both initial reservoir temperature T Res,Ini and inlet fluid temperature T i were 20 °C. Figure 7 shows the temperature of water exiting the reservoir over 6 hours for three different solar collector areas. The initial power P int supplied by the three solar heat collectors is 0 W to simulate night. Solar power is assumed to increase linearly over a 6 h period from 0 to 750 W m -2 , and the ramped powers P ramp depend upon solar collector areas. The   Table 4.

Conclusions
The DFHXM produces accurate models of a variety of DF heat exchange systems, but the user should note that it functions best in situations with small reservoirs and high flow rates because temperature in the heating reservoir is approximated as uniform throughout. The user should also note that both temperature and residence time affect the elimination of Legionella; special care should be taken to ensure that fluid reaches a killing temperature for a specified time in the DF system. Although the DFHXM makes many simplifying assumptions, it nevertheless accurately models the transient and steady-state behavior of DF heat exchange systems. It has potential to be a valuable but inexpensive resource to anyone with access to Microsoft Excel. Legionnaires' disease will likely be an increasing problem as more and more energy efficient hot water systems are installed, and a DF heat exchange system may be an energy and cost effective treatment alternative to other control methods. Additionally, use of solar water pasteurization will likely increase as global populations rise and the need for safe water becomes larger. The DFHXM has the potential to assist many users with a wide variety of design problems. Current and future work includes examining the energy-usage and costs of DF heat exchange systems for pasteurization in Legionella spp. infected hot water systems, and initial results show that in certain design scenarios DF heat exchange systems are more energy and cost effective than current disinfection methods.