Solar Thermal Cogeneration
[Overview] [Program] [System] [Collector] [Turbine] [Generator] [Controller] [Battery]



The Solar Thermal Cogeneration (STC) system provides electric and thermal energy from solar energy for a conservation-oriented residence.  Thermal applications include space heating/cooling, food refrigeration and hot water heating.  For economy, the STC is optimized for the characteristics of the residential structure and the climate.  It is intended for a passively heated/cooled residential structure in a hot arid climate but may be adapted to other structures/climates.  It employs a low profile solar collector to be installed on a flat roof and mostly hidden from ground view by the roof parapet.   

System Overview

The STC system includes a parabolic trough solar collector, with steam as the working fluid driving a bladeless turbine that drives a permanent magnet generator.  The generator charges batteries through a charge controller, integrated with an AC inverter and DC converters that supply the residential power.  30 to 40% of the steam's energy is converted to electric energy and the remainder is transferred as thermal energy by the condenser for heating and cooling purposes.  Cooling is provided by an ammonia/water absorption cooler, driven by the condenser heat.  Thermal banks provide 24-hour availability of thermal energy for end-use.  A fuel pre-heater provides a supplemental energy source for overcast days.  In night sky cooling mode, the solar collector radiates waste heat to the night sky.  The following diagram illustrates energy flow in the system.

system diagram

Steam Subsystem

The STC's steam subsystem is a closed loop Rankine cycle heat engine consisting of a boiler pipe, turbine, condenser and a feedpump returning water to the boiler.  As the boiler water absorbs heat and changes to steam, pressure builds and pushes the steam toward the turbine nozzle.  Past the nozzle, a lower pressure is maintained by the turbine/condenser.  At the nozzle, the pressure differential accelerates the steam to a high velocity/energy and the steam imparts some of its energy on the turbine rotor, propelling the turbine shaft and reducing the steam velocity/energy.  The steam is drawn to the condenser by the vacuum of condensation where it changes to water on the condenser's heat exchange surfaces.  The feedpump returns condensed water to the boiler with a forward pressure that keeps the boiler steam from backing up. 

The STC's solar collector receiver pipe serves as the steam boiler.  This type of boiler is known as a monotube or once-through boiler because the water/steam is completely contained in a small diameter pipe, without water reservoirs.  Traditional boilers use reservoirs to ensure that water is always present on the opposite side of the boiler heating surface.  This keeps the material's temperature lower, allowing the use of lower-cost materials.  In contrast, the monotube allows the water to boil to steam inside the tube being exposed to the heat source.  Steam has a much lower coefficient of heat transfer than water and cannot as effectively cool the tube material, so the monotube requires higher-strength material.

Traditional boilers are also fitted with blowdown systems and other features to allow the use of untreated water.  Monotube designs eliminate these components and rely on water treatment and a closed-loop steam cycle that preserves the treated water.  Because a monotube is quick reacting to changes in heat input, tight control of the feedpump is required to maintain a steady water fillpoint (phase change point) along the receiver pipe to isolate temperature/pressure transients/stresses to a shorter section of the pipe.  A digital control/monitor subsystem helps ensure operation within rated bounds and predictable component lifespans.

The steam energy available to power the turbine is proportional to the steam pressure, which is roughly proportional to the product of mass density and temperature (1).  But temperature and pressure are limited by several things:  The necessity of a low-profile collector requires a long length receiver pipe and the pipe diameter must be a practical size.  Since heat loss per unit area increases with the fourth power of temperature *, heat loss from the pipe can be excessive at higher temperatures.  High temperature materials and strategies to limit heat loss are very expensive.   So a low-cost line-focus collector must rely on a greater mass flow of lower temperature/pressure steam than other designs, namely the point-focus collector.

The line-focus collector's reliance on greater mass flow affects the turbine design and likely increases the necessary receiver pipe length and thickness, and the feedpump load, compared to an equivalent capacity point-focus collector that relies on hight temperature/pressure.  But the line-focus collector's full costs may be lower due to lower temperature/strength requirements on the materials.  The various advantages of low-profile roof mounting and low-cost materials may offset the efficiency disadvantage.

The turbine load is ideally set to draw the superheated steam down to as close to saturation as possible because saturated steam has greater thermal conductivity, and thus condenses more efficiently.   In the winter the system must operate as efficiently as possible over the wider range of energy rate each day.  So in the winter, the receiver temperature and the turbine load should both be maintained proportional to the input energy as it varies across the day, to keep the steam saturation/condensation at maximum efficiency.
On load changes the turbine/condenser pressure changes.  If the turbine nozzle sees a pressure drop that's less than its critical pressure drop, the downstream pressure affects the mass flow through the nozzle.  Changes in mass flow significantly affect the upstream pressure because monotubes have small volume capacity relative to flowrate.  So a rapid load decrease, without corresponding source energy and flowrate decreases, causes a rapid evaporator pressure increase, changing some steam back to water.  And a rapid load increase causes a rapid evaporator pressure decrease, changing some water to steam (2).  A change in source energy, such as when a cloud blocks the sun, can also cause a rapid pressure decrease.  These conditions cause the water fillpoint to move rapidly along the receiver pipe, which then alters the heat transfer rate in the affected evaporator section, creating a rapid temperature change and thermal stress on that section. 

To minimize the number of pipe sections undergoing high thermal stress and requiring high-temperature material, and to minimize transients that stress the overall system, the fillpoint should be kept in a narrow range of the receiver circuit.  The system can react to transient conditions and stabilize the fillpoint by changing the flowrate, smoothing the loads with the load controls, and defocusing concentrator sections when necessary.  The load control capability is in addition to the smoothing capacity of the stores (batteries and thermal banks).  The load controls can also limit steady load demands to prevent long-term operation in an overload condition.

Since lower flowrates require less feedpump power, and higher temperatures provide better heat transfer, the system maintains as low flowrate and as high temperature as allowed by system ratings and which satisfies the negotiated energy transfer and maintains the water fillpoint. 

(1) When the steam is superheated, the ideal gas law applies but in the phase transition region, water vapor adversely affects accuracy of the model's predictions. See (3).
(2) The ideal gas law states that for most gases in most situations, the ratio of pressure to temperature is proportional to density, or mass per volume.   For a gas, if the pressure increases or the temperature decreases, density increases, volume decreases and the gas may change to liquid phase.  For a liquid, If the pressure decreases or the temperature increases, density decreases, volume increases and the liquid may change to gas phase.  These phase changes can happen rapidly and unexpectedly, especially on pressure changes, and can cause severe stresses on the steam system. See (3).
(3) The ideal gas law may be improved upon with much more complex formulas such as the freesteam: IAPWS-IF97 formula [* |*].

Clayton (Once-Through) Steam Generator
IST (Once-Through) Industrial Boilers

Supercritical Pressure?

The boiler's evaporator section piping undergoes great stress from rapidly fluctuating temperature gradients between the outside and inside surfaces due to the rough nature of the water to steam phase change.  This problem calls for expensive stainless steel pipe material to handle the rapidly fluctuating temperature gradients.  Supercritical pressure allows the boiler water to maintain a liquid state at temperatures higher than the atmospheric pressure boiling point, carrying a comparable amount of energy as steam to the turbine, potentially eliminating the need for expensive stainless steel pipe material.  A large temperature gradient remains between the outside and inside surfaces of the pipe but the fluctuations are nearly eliminated.  The water flashes to steam only at the turbine nozzle where velocity helps to ensure a much smoother phase change and in an area where the temperature gradient is much smaller. 

The water temperature in the pipe must be carefully limited to avoid saturation, e.g. if the pressure were 1000 psi, the temperature must be kept significantly below 544
°F.  Given a source energy rate of 220kBTU/day (10 BTU/s) and 1/2" pipe, the  supply water is 2 cuin/s, and the feedpump load is 400 lbs, drawing 400 lb * 10 in/s = 340W of electric power.  This is about 30% of the electrical output at this source energy rate.  Carbon steel pipe has a working pressure of about 250 psia (Sch40) and 750 psia (Sch80) at 400°F.  Clearly an electrical feedpump and carbon steel boiler pipe are inadequate at this supercritical pressureSch80 carbon steel may be used at intermediate pressures.  To reduce the feedpump load to 5% of electrical output, the pressure and temperature would have to be lowered significantly and compensated with increased volume flow rate.  Supercritical pressure is probably worth further investigation but for now this document will cover the conventional two-phase boiler.

Other approaches that avoid high thermal stress phase changes inside the boiler tubes have been employed or investigated for parabolic trough solar thermal systems.  One is the use of high temperature oil in the receiver tube that remains in a liquid phase and heats a conventional Rankine steam system through a heat exchanger.  The oil approach has a few issues as listed here, with the fire hazard seeming too much for a residential application.  Another all-steam approach separates the liquid phase section and the gas phase section of the monotube boiler with a reservoir evaporator that prevents phase change in either section.  This approach may allow for a simplified control scheme and higher reliability at the cost of a reservoir and possibly additional components.  But the simplest approach is probably the straight monotube with the evaporator sections replaced periodically over the system lifespan, if necessary.

Sensor/Control Components

Sensors: The solar focus sensors attached to the receiver pipe are used to focus maximum available solar energy on the receiver pipe.  The load demand sensors include battery current and coolant temperature sensors used to determine changes in load demand.  The turbogen rpm sensor is an electronic component of the charge controller and used to maintain the turbogen's max-power rpm (1) and estimate energy transfer.  The receiver temperature sensors are thermocouples attached to the outside surface of the receiver, one per section, supplying a temperature profile across the receiver to monitor the water fillpoint and protect the receiver from overheating.  The receiver temperature profile and the feedwater flowrate sensor in the feedpump controller are used to maintain the temperature and flowrate within rated bounds while optimizing them (high temperature and low feed rate) for most efficient energy transfer. 

Controls:  The source energy control continually adjusts the concentrator's tracking mechanism to seek the maximum available energy from the sun as it moves across the sky.  When the load demands wane, some of the concentrator sections are taken offline to lower the energy input, or the system is shut down entirely (2).  A tracking offset might be used to reduce the energy transfer but this is a problem for birds/pilots and will only be used for temporary overheat protection.  The feedwater flowrate control continually adjusts the feedpump to accommodate varying energy transfer rates while maintaining system parameters within rated bounds.  The load controls include the battery charge controller, which is able to attenuate the electrical load seen by the generator through solid-state switching techniques, and the coolant flowrate controls for the condenser's heat exchangers.  These controls allow the system to seek most efficient energy transfer and maintain rated bounds of system parameters as load demands and available energy rise and fall in relation to each other.  

(1) When the thermal load demand (heating/cooling) is high and electrical load demand is low, the system will allow a deviation from max-power rpm to a rated limit to accommodate the thermal demand.
(2) There may be an energy surplus in the summer.   Summer surplus may be avoided by waiting until winter to polish the aluminum concentrators.   But it's likely that a household can find a use for the summer surplus.  For example, a hybrid electric car might get a summer boost. 

Steady-State Operation

Control Scheme:  To be maintained are the water fillpoint in the receiver pipe, steam temperature and water flowrate within rated bounds, and maximum energy transfer with minimum mechanical/thermal stresses.  Energy transfer is usually limited by available source energy but sometimes there will be a surplus.  For minimum mechanical/thermal stresses, the Control/Monitor Subsystem sets the load controls to meet as much of the load demand as the available energy can accommodate, with the maximum steam temperature and the minimum water flowrate and the turbogen's max-power rpm, all within rated bounds. 

Control Loop:
When something changes, adjust load controls, feedwater flowrate and solar tracker in appropriate reaction to satisfy load demand with maximum steam temperature and minimum water flowrate while maintaining water fillpoint, turbine max-power rpm, and system ratings.

Startup/Shutdown Operation

In the morning, when sun light is strong enough, the concentrator begins focusing.  When the receiver pipe starts heating up, the feedpump fills the transfer pipe to the receiver inlet.  When the first receiver section temperature sensor indicates the water has reached the receiver the feedpump pumps slow enough to avoid flooding the receiver but fast enough to avoid overheating the receiver.  As the water temperature gradually builds toward saturation, vapor gradually fills the vacuum and preheats the turbine/condenser.  This takes place over the course of one to two hours with minimum load on the variable-speed feedpump.  A slow warm up/cool down of all components is important to minimize thermal stress.  As the pressure builds in the receiver the feedpump maintains the water level which the receiver temperature profile indicates.  When the temperature profile indicates that the steam is reaching a certain dryness at the end of the receiver, the condenser coolant pumps start and slowly draw down the pressure in the condenser.   The controller completely attenuates the turbine load, freeing it to spin up as the velocity of the steam through the turbine nozzle gradually builds.  The turbine load is gradually increased in proportion to the developing source energy.  As the receiver pipe (boiler) pressure builds and the flowrate increases, the water fillpoint becomes compressed into a narrower section of the receiver pipe. 

Shutdown is also a gradual process.  The controlled loads and the feedpump gradually taper off as the source energy wanes.   When the feedpump stops the steam in the system condenses, the vacuum returns and the water slowly drains back into the condenser reservoir.  The rest of the system's volume is under vacuum during shutdown.

Automatic Control of a 30 MWe SEGS VI Parabolic Trough Plant (pdf)


A basic Rankine cycle component, the condenser creates a low pressure region in the turbine outlet, enabling a high pressure differential which drives the static to kinetic energy conversion at the turbine nozzle.  The condenser also returns the steam out of the turbine to water for reuse in the steam loop.  The steam is condensed to water also so that it may be pumped efficiently against the boiler pressure.  Condensation is driven by heat exchangers that draw heat from the steam for various residential heating/cooling applications.  If the condenser maintains a pressure below 1 atm, the condensation temp. can be much lower than 212°F, and increase the cycle's thermal efficiency accordingly.  The goal is to condense with greatest efficiency and reliability at lowest material cost over a wide range of steam temperatures/pressures and load demands.   To maximize overall system efficiency, the condenser should be well-insulated and unnecessary subcooling of the condensate should be avoided.

The condenser contains heat exchangers in circuit with the hot bank and with the absorption coolers. These exchangers must be arranged for each to have efficient heat transfer with the steam.  Heat transfer efficiency should be high in order to minimize material costs and minimize the coolant circulation load.  This efficiency is affected most by the temperature difference between the steam and the coolant, determined by the system design.  Appropriate coolant turbulence and flow rate are also important.  The turbulence of a wide radius coil aids heat transfer, while the turbulence of a sharp bend wears pipe and wastes energy.  Heat transfer is enhanced by making the heat transfer surface area as large as practical, ensuring uniform distribution of steam across it, minimizing scale/oxide on it, and minimizing air (non-condensibles) in the steam system. 

Saturated steam transfers heat much more efficiently than superheated steam, so the more saturated the steam leaving the turbine, the better.  The material and thickness of the heat exchanger tubes affect heat transfer.  Counterflow of the fluids in heat exchange generally improves heat transfer and reduces thermal stress.  Counterflow also allows a decreasing temperature/pressure gradient along the heat exchange surface in the direction of steam flow which enhances the flow rate. Turbulence in the steam flow is important for heat transfer efficiency and is achieved with fins or baffles.  The heat exchanger tubes and baffles should channel the steam toward more tubes, and away from the condenser shell.  Though turbulence aids heat transfer, it also decreases the pressure differential seen by the turbine/generator so experiments in condenser geometry should be performed to achieve an optimum balance.

The condensate water level in the reservoir below the coolant tubes should not be allowed to rise and and block steam from reaching the coolant tubes.  The reservoir must hold all of the steam system water when the system is not operating.  A deeper reservoir provides more gravity forward pressure to reduce feedpump cavitation risk.  But the reservoir's vertical height and placement must allow for gravity drain of the water when the system is not operating.

A common condenser design is a cylindrical shell with straight coolant tubes around which the steam flows with condensate exiting the bottom of the shell.  Another design is the helical coil which may increase heat transfer by 40% over the straight tube condenser by inducing turbulent flow in the coolant.  The STC's turbine might be placed vertically over the condenser housing, so that the turbine outlet feeds into the center of the condenser and condensate drains into the reservoir. 

Another type of condenser is direct-contact or jet condensers, which are very compact, and very efficient in an open-cycle, but in a closed-cycle the condensate must be cooled by another heat exchanger to be re-used in the jet.

Condensing steam creates a vacuum which pulls air into the system through microscopic leaks in the condenser shell.  Proper fitting of connections is a must.  Air in the system can corrode the pipes and reduce heat transfer by reducing the steam pressure/temperature or forming insulating films on heat exchange surfaces.  A vacuum procedure is necessary to remove air and maintain vacuum, possibly automated but probably applied manually on a periodic maintenance schedule.  Also, water is lost through microscopic leaks in the pressure sections of the system and should be replenished on the same schedule. 

Surface condenser
Specifying Steam Surface Condensers
Large Steam System Condensers
Steam Engineering Principles and Heat Transfer
Thermodynamics Ch3 - WesTrain (pdf)
Condenser Basics (pdf) (direct contact type)


A basic Rankine cycle component, the feedpump keeps the boiler fed with water from the condenser.  The feedpump must work against the boiler pressure and condenser suction which are significant, making the feedpump efficiency a high priority.  Additional loads include pipe friction and flow constrictions and these should be minimized.  The feedpump must quickly respond to changes in boiler pressure and operate reliably and with high efficiency over a range of flowrates and pressures.  The feedpump and feedwater lines should be well-insulated to minimize heat loss. 

Pumps are rated in terms of power draw, flow rate and pressure.  Power draw (horsepower) equals flow rate (U.S. gallons per minute) times pressure (feet of head, one ft. = 0.433 lbs/in²), divided by 2178.  Pump manufacturers typically produce a plot of flow rate versus pressure for a standard speed, often 3600 rpm, and a set of curves for individual pump rotor diameters.  The rotor diameter is selected by locating the pump curve closest to the intersection of the application's primary flow rate and pressure.  The motor horsepower is similarly selected from sloped horsepower lines on the plot. 

Since the solar application involves a range of flow rates and pressures, the rotor diameter and motor horsepower should be selected to handle the maximum sustained load, and a permanent magnet motor and variable frequency drive (VFD) should be used.  Due to the boiler pressure, some designs integrate the feedpump onto the turbine shaft.  But this complicates the turbine design and requires a control valve and a separate startup pump.   Electric pumps can be very reliable and can justify the required energy conversions, especially in an application that requires a wide range of flow rates.  The VFD can instrument the boiler flow and pressure for the system controller.  The VFD is capable of quick response to unpredictable source/load changes and capable of gradual speed changes that minimize stresses.

Cavitation is the growth and collapse of gas bubbles in the liquid being pumped, causing inefficiency, wear and noise in the pump rotor.  It results when the liquid pressure is lowered to its vapor pressure during its acceleration by the pump rotor.  Cavitation is a concern in closed steam cycle feedpumps due to a tendency for high temperature and low pressure in the pump feedwater.   Higher temperatures result in greater cavitation risk because the vapor pressure increases with temperature. 

Two ways to reduce cavitation risk are to lower the temperature and increase the forward pressure of the feedwater feeding the pump.  But lowering feedwater temperature reduces system capacity for electric generation and absorption cooling.  Gravity may be used to increase forward pressure by mounting the feedpump a distance below the condenser reservoir. 

Centrifugal pumps are capable of up to 90% efficiency in applications with more static pressure and less fluid velocity, such as boiler feedpumps.  Closed-impeller types are more efficient than open impeller types.  The pump outlet should be large to maintain the static back pressure that makes the pump efficient.  A spiral volute performs this function with a conical reducer connecting that to the boiler pipe.  A bladeless pump is a simplified centrifugal design that is easy to construct and less prone to cavitation.  Regenerative turbine pumps and radial-vane pumps are good for high-pressure, low-flow applications.

Understanding Pump Cavitation
The Internet Glossary of Pumps
MTH Pumps - Boiler Feed Service
Pumps - Engineering Toolbox
Affinity Laws

Fuel Pre-heater

When extra capacity is needed, the solar energy is supplemented with a feedwater pre-heater.  The pre-heater consists of a coiled tube in line between the feedpump and the receiver, heated by a pulsed flame.  The pre-heater supplements solar energy during the off-peak periods of the day (when the sun is lower in the sky) to effectively extend the period the system operates at peak capacity. The flame is pulsed by the system controller with a duty cycle that provides the amount of supplemental heat needed to reach peak capacity.  modulating burner?  The system could be programmed to recover a day's full output after intermittent clouds or supply a temporary demand surge.

Thermal mass in the pre-heater smooths out the temperature change. Inside and outside the tube coil are radiation reflectors, and beyond those, heavy insulation.  To avoid expensive materials, the pre-heater would not make steam, so during extended periods of overcast sky, electrical end-uses rely on batteries and food refrigeration relies on ice.  During these periods, the remaining hot bank heat is expended in tap-water & space heating, then the pre-heater re-charges the hot bank.  In this mode the feedpump simply pumps water through the steam loop during the day.  Space cooling is typically not needed when the sky is overcast.

A steam-making fuel-fired auxiliary boiler could be beneficial in cloudy climates.  It could fully supply the STC's rated output on overcast days, provide supplemental energy on clear days when needed, and reduce the required storage capacity (electric and cooling) to 24 hours.  The auxiliary boiler would be a high-temperature tube coil  in line between the feedpump and the receiver.  25% of the energy may be lost from the receiver which is a significant disadvantage.  Another disadvantage of the steam-making configuration is the expense of the high-temperature boiler tube.

The STC may remain completely carbon-neutral, with minimum emissions by burning vegetable oil in the supplemental heater from plants such as jojoba, produced with low-energy methods.

Absorption Cooler

Cooling cycles use energy to transfer heat from colder areas to warmer areas.  Cooling cycles are used for food refrigeration and space cooling.  Vapor-compression coolers use mechanical energy to drive the cooling cycle.  Absorption coolers use heat energy to drive the cooling cycle.  Absorption coolers serve cooling applications where heat is more available than electricity.  Absorption coolers are quiet, reliable and economical, requiring only small amounts of electric power for pumps, and having around twice the maintenance interval, and as low as 10% of maintenance costs as vapor-compression coolers *.  Absorption coolers maintain relatively constant efficiency over a range of cooling capacities compared to  vapor-compression coolers * (pdf).  Absorption coolers are CFC-free, utilizing a refrigerant/absorbent, with ammonia/water being an effective choice for water-freezing temperatures, a requirement in the STC application.  When full costs are considered, absorption coolers can be more economical than vapor-compression coolers, even when energy costs are equal.  When a cheap source of heat is available to drive the absorption cooler, it can be far more economical.  Plenty of excess heat is available in the STC's steam condenser to drive absorption coolers for food refrigeration and space cooling. 

The generalized cooler consists of an evaporator, a compressor, a condenser, and an expander in a closed circuit containing a working fluid.  Vapor-compression coolers use a mechanical compressor while absorption coolers use a thermal compressor consisting of an absorber, pump and generator.  In the ammonia absorption cycle (see figure), NH2 liquid is evaporated at low pressure, drawing heat from the cooling application, then the NH2 vapor is absorbed by water, producing waste heat. This mixture (aqua), driven by a small, low-power pump, then draws heat from the external driving source, generating ammonia vapor at high pressure.  The ammonia (NH3) vapor is rectified into NH2 vapor which is then condensed and expanded to low-pressure liquid, producing waste heat, and the cycle repeats. 

Absorption coolers are designed with various levels of efficiency, single effect, double effect, etc.  Double effect is driven with a higher temperature heat and has primary and secondary sets of generator, rectifier, and condenser, with the primary condenser heat driving the secondary generator.  Single effect delivers a coefficient of performance (COP) up to 0.7 while double effect delivers a COP up to 1.0.  The steam temperature exiting the STC's turbine is probably not high enough to drive a double effect cooler.  The COP of the single effect ammonia absorption cooler may be around 0.5 if the cooler's waste heat is rejected to hot ambient air and probably around 0.7 if rejected to a relatively cool thermal bank [1]. 

Absorption coolers can operate over wide temperature ranges but efficiency depends on the the generator (heat source) temperature, absorber/condenser (waste heat) temperature and the evaporator (cooling application) temperature.  A higher generator temperature allows for a lower evaporator temperature.  The maximum COP is [(Th-Tm)/Th]*[Tl/(Tm-Tl)], where Th = high temp (heat source) (K), Tm = mid temp (waste heat) (K), and Tl = low temp (cooling application) (K) *.  Larger Th -Tm improves condenser heat transfer and smaller Tm - Tl improves evaporator heat transfer, both improving maximum COP.  As such the absorption cooler is best operated in the morning when its heat sink (hot bank) is relatively cold.

A typical space cooling load is 53 kWh/day.  Given a COP of 0.7, the cooler's total waste heat is the driving heat plus heat from the cooling application, or (1/0.7 + 1)*53 kWh/day = 128 kWh/day.  Ideally, all waste heat is stored in the hot bank so it may be emitted at night.  But if the emission rate is not enough, the waste heat might be expelled to the air during the day.

To compare absorption and compressor coolers in the STC application, an absorption cooler increases the cost of expelling the steam system waste heat by effectively lowering its temperature.  A compressor cooler draws significant electrical energy away from other applications, and converts the electrical energy into additional waste heat to be expelled.  For example, a typical compressor cooler has a COP of 3 so the electric energy needed for 53 kWh/day of space cooling in the above example is 17.6 kWh/day.  This is 28% of the 62 kWh/day of electric energy produced by the prototypical STC system. After these costs are compared, along with the various other pros/cons of the two approaches, a choice between the two types of cooler may be made.

The absorption cooler is positioned near the STC's steam condenser to minimize heat loss in the aqua lines.  Cooler waste heat is removed by heat exchangers to the STC's hot bank.  A coolant fluid circulates between the cooler's evaporator and the cooling application heat exchangers.  The cooler's evaporator may be positioned near the cooling application to minimize heat gain in the coolant lines.  For food-freezing temperatures a good coolant is a mixture of pure water and an appropriate pure alcohol.

The absorption space cooler may also perform space heating, if configured as a reversible heat pump.  Reversible heat pumps have much higher COPs in heating mode than in cooling mode because the compression work adds to the heat output.  This greatly increases the STC's space heating capacity with a relatively small increase in system complexity, utilizing the absorption subsystem which would otherwise remain idle in winter.  The only needed modification appears to be re-routing the night sky cooling circuit for the absorption subsystem's evaporator to draw heat from the winter air. 

Another approach to space cooling is the evaporative or swamp cooler which relies on the evaporation of large quantities of water to cool air, with no other inputs needed except energy to pump the water and circulate the air.  It is most efficient in lower humidity arid regions but given water shortages this might not be the best choice for a new installation.  In humid climates a de-humidifying function is needed in space cooling to prevent a clammy feeling in the cooled space.  De-humidifying is costly, but efficiency increases with lower temperatures.   The STC is able to produce the temperatures needed for absorption cooling to perform efficient de-humidifying.  Many natural building materials help regulate humidity.

Cooling technology
Ammonia Absorption
Waste Steam to Power Absorption Chillers (pdf)
Chose - Absorption chillers (pdf)
[1]Optimization of a solar ammonia-water absorption chiller (pdf)
New Gas-fired Heat Pump Technologies Help Chill Greenhouse Effect

Thermal Banks

The STC's thermal banks are well-insulated hot and cold water (1) tanks that store thermal energy for end-use applications that require 24-hour availability.  60% of the energy in the steam is available at the condenser for use in thermal applications.  The absorption cooler first draws heat from the condenser for the cooling applications and outputs heat to the hot bank.  The hot bank then draws the remaining heat from the condenser and stores it for use in heating applications.  The hot bank heat that isn't used for heating applications is dissipated by night sky cooling.

Thermal storage capacity is a function of specific heat, mass, and temp. at full charge/discharge.  The hot bank's thermal storage capacity should accommodate the total heat output from steam condensation and absorption cooling for one summer day.  In higher latitudes, more capacity is used in summer, resulting in a high charge temp. and a high charge/discharge differential.  Less capacity is needed in winter, resulting in a low charge temp. and a low charge/discharge differential.  If the winter charge temp. is not high enough round-clock to serve end-uses appropriately, then a separate tank may be used for those.

The tanks may be cylindrical, which is the strongest geometry that is easy to fabricate.  The cylinder of minimum surface area (minimum heat loss/gain and minimum material cost) for a given volume has equal height and diameter.  The diameter (ft) = 0.5542 * gallons^(1/3). A cylindrical tank should be mounted vertically for even distribution of forces.  From Laplace's law and the static pressure formula, the tension due to gravity on the wall of a vertical cylindrical tank of water, with radius r, and at depth d (m) is: t = 9810 × d × r (N/m).  The tanks and piping may be carbon steel for strength and should be well-insulated.  Corrugated sheet for the side wall may have greater strength for less material.

The tanks should contain pure water to minimize corrosion.  Gas-induced corrosion depends on material type, temperature and temperature flux, and concentration of dissolved gases (oxygen and carbon dioxide).  Gases also reduce heat transfer efficiency.  To keep dissolved gases below 1 ppm for carbon steel, the system should be sealed.  But the water volume changes by 4% across its full liquid phase temperature range (at 1 atm pressure) due to thermal expansion.  The hot bank will utilize most of this range in summer. 

A sealed water heating system is typically fitted with a thermal expansion tank containing a flexible rubber diaphragm sealing an air space that compresses to accommodate the thermal expansion.  The air pressure is set to maintain the working system pressure.  The STC's thermal banks only need a small positive pressure to discourage air ingress, e.g. at the pump seals.  A diaphragm may be fitted in the main tank, e.g. a smooth hemispherical dome under the tank top, but this diaphragm must endure both temperature cycling and water turbulence.  So a separate expansion tank connected with an anti-thermosiphon pipe loop is probably better.  In such a tank, the pipe connects at the bottom, and the hemispherical diaphragm flexes upward when the water expands and conforms to the hemispherical tank bottom when the water contracts.  The cold tank corrosion is much slower and expansion much smaller. 

All inside surfaces should be very clean and free of defects, burrs and contaminants, including pipe dope.  Dielectric Insulators may be needed to prevent galvanic corrosion on steel to copper connectors.  A heat exchanger might be required inside the hot tank, e.g. for heating tap water, but for general heat transfer the thermal bank water flows in loops with heat exchangers connected at the ends.  To exploit temperature stratification in the tanks:  Send cold water from the bottom of the tank and return hot water to the top of the tank;  Send hot water from the top of the tank and return cold water to the bottom of the tank (2). 

Linear thermal expansion in the pipes is accommodated by turns or with loops.  Pipes should be short to minimize material costs, pump loads and heat loss/gain.  Pipe bends should be wide radius to minimize turbulence.  Closed loops have friction head and buoyancy head but no gravity head.  The pump load due to friction head has to be balanced against material costs and heat loss/gain in the choice of pipe diameter.  Buoyancy head only slightly increases or decreases the pump load, but may create a thermosiphon heat loss/gain path when the pump is off.  To minimize buoyancy head, but mainly for space economy, the tanks may be stacked, with hot on top. 

The loop pumps should be highly efficient and not introduce any contaminants.  To minimize cavitation, a pump should be placed in the loop where fluid and ambient temperatures are moderate and suction head is minimum (e.g. fed directly from the tank).  This also reduces air ingress through fittings by suction head.  Bladeless pumps with permanent magnet motors and variable frequency drives may be used with flow rates dynamically optimized by the control/monitor subsystem.

To minimize heat loss/gain, position the tanks away from heavy masses, insulate nearby masses, shelter from sun/wind and otherwise limit air flows.  Passive-solar building approaches and seasonal adjustments are probably worth a look.  See Locating the Thermal Banks

An example configuration for the various residential thermal applications includes a food refrigerator/freezer with an ice bank, radiant floor tubes for space heating , radiant ceiling tubes for space cooling and "on-demand" tap water heating through a tube coil in the hot bank.  The tap water temp. is safety limited by thermostat-controlled mixing with cold water. The space cooler makes a circuit with the cold bank.  The ice bank and the cold bank each make a circuit with the absorption cooler, which makes a circuit with the condenser.  The space heater makes a circuit with the hot bank, which makes a circuit with the condenser.  Each of the circuits' heat transfer rates via volume flow are under control of the control/monitor subsystem with thermocouple monitoring and thermostat input.

Hot bank sizing example:  During the summer the prototypical STC system provides 139 kWh/day for thermal applications, of which11 kWh makes hot water, so 139 kWh - 11 kWh = 127 kWh is available for cooling applications.  The absorption coolers extract 53 kWh from the cooled space plus 5 kWh from food refrigeration for a total of 58 kWh.  Added to this is (1/0.7)*58 kWh = 83 kWh of heat driving the coolers for a total of 141 kWh of lower temp. heat from the coolers to be held in the hot bank.  Added to this is the remaining 127 - 83 = 44 kWh higher temp. heat from the steam condenser for a total of 185 kWh of heat to be held in the hot bank.  Given initial and final hot bank temps. of 93°F and 140°F the temp. differential Td = 26°K.  These temps reflect a balancing of the absorption coolers and night sky cooling efficiencies using the parameters specified in the night sky cooling section below.  Using the specific heat of water, c = 4.396 Wh/(gal*°K), the hot bank capacity needed to store this energy (3) = E (Wh) / (c Wh/(gal*°K) * Td(°K)) = 185,000 / (4.396*26) = 1600 gal.

A tank of this size (6ft height, diameter) may be constructed in the ground using perlite insulation and bentonite clay sealer.  The top may be made from wood.  This tank holds the waste heat from both the absorption coolers and the steam condenser for night sky emission.  It's likely that a separate smaller tank with a higher average temp. is needed for winter space/water heating.  Alternatively, a single tank may be sized to accommodate winter space+water heating and excess steam condenser heat, with night sky emission, and separate forced-air coolers for the absorption coolers.  Alternatively, a single tank may be sized for winter space+water heating, and connected to the steam condenser, absorption coolers, and a forced-air cooler (see table).  A choice is made by assessing the material, space, energy, and environmental costs of the tank/coolers for each alternative.  Later expansion of heat end-uses may be taken into account.  A more fully developed option uses two hot tanks, one 600 gal. and one 700 gal. with night sky cooling (details).

Cold bank sizing example: Given daily heat from the cooled space of 53 kWh (1.5 tons @ 10 hrs/day), and initial and final cold bank temps. of 40°F and 80°F, temp. differential Td = 22°K.  The cold bank need only store half the total space heat because the other half is ejected directly during the day, so the cold bank capacity = 26,500 / (4.396 * 22) = 274 gal. 

(1) Water is an effective thermal storage medium, having a higher specific heat capacity than most others.
(2) In the case of the hot tank sinking heat from the condenser during the day and sourcing heat to the condenser at night, a one way pump allows exploiting stratification in only one of the two periods.  In
summer, higher efficiency is needed at night to minimize battery discharge, especially given the extra heat from the absorption cooler.  In winter, higher efficiency is preferable during day, given much less heat is to be rejected at night.  Given the relative surplus of electric power in the summer, it's probably better to exploit stratification during day, and pump cold water from the bottom of the tank to the condenser.  A baffle, consisting of a horizontal plate in the tank, can encourage the incoming cold water to mix instead of rapidly sinking to the bottom.
(3) for water, it takes 1 calorie to raise the temperature of 1 gram of water by 1°C

Night Sky Cooling

The STC must eliminate excess heat from the condenser that isn't consumed in heating applications.  The STC may hold the excess heat in the hot tank and reject the heat to the sky at night through radiation to the sky, and natural convection to the air.  Compared to using the daytime air as a heat sink, night sky cooling provides the steam system a lower condensation temp. resulting in greater Carnot efficiency and throughput for a given boiler temp.

Night sky cooling may be accomplished through a fluid tube thermally connected to the back of the solar concentrator which is painted with an emissive coating, and exposed to the sky at night by solar tracking adjustment.  The solar concentrator as a heat exchanger convects more heat to the air than it radiates to the sky, but the night sky is typically a much colder heat sink than the local environment (1) so a significant percent is radiated.  This reduces the STC's contribution to terrestrial heating and particularly benefits the local microclimate in the summer.  Night sky cooling provides an opportunity for space cooling through natural heat transfer from the cold bank to the night sky without the need for an active cooling cycle.  And if the condenser waste heat is to also be emitted to the sky, the absorption cycle enables a higher overall transfer rate that allows both. 

Night sky cooling achieves a savings in materials and digging costs over a ground loop heat exchanger.  A reduction in energy draw and noise is achieved over a forced air heat exchanger.  However when operated at night from the hot tank, the forced air approach uses less materials.  Forced air running during the day eliminates the hot tank, but requires a lot of materials, consumes a lot of energy, and produces a lot of noise and high heat which may affect the local microclimate in the summer.

Heat radiated by atmospheric gases, mostly water vapor and carbon dioxide, limits the radiation potential from terrestrial objects to the night sky.  The amount of heat transfer from a terrestrial object to the night sky increases with the difference between the object and atmosphere temps.  The effective sky temp. is typically 10 °C to 20 °C, and as much as 30 °C below the ambient temp. (2), seeming to fall with ambient temp. but at a greater rate.  The effective sky temp. depends mostly on the amount of water vapor and carbon dioxide in the atmosphere, the temps of the various atmospheric layers, and the ground level, altitude, ambient air temp. and humidity.  Clouds can make the sky temp. approach the ambient temp.  In a humid climate, the dewpoint temp. may reach so high as to cause condensation on the emitting surface, which heats it and lowers the system's cooling capacity. 

A small pump circulates fluid from the hot tank through the night sky cooling tube circuit.  The tube is relatively thin aluminum and runs straight along the back side of the concentrator for its full length, soldered for best thermal contact.  After assembly, the components are painted with an emissive coating to maximize radiative heat transfer.  At the end of each collector section a flexible rubber tube is formed in a loop to allow for a difference in the tracking adjustment for each section. The fluid should probably be a mixture of pure water and an appropriate pure alcohol to avoid freezing in winter.

The emissive surface area is the total length of the collector field times the circumference of the parabolic concentrator.  Since the solar tracking mechanism uses the concentrator's focal point as the axis of rotation, the concentrator's frame is simplified by setting its depth equal to its radius, which makes circumference = 1.15 * width.  The curvature of the concentrator keeps most of the surface area off-angle to the zenith, reducing the effective radiative heat transfer by directing more of the radiation to the warmer terrestrial environment, so the effective surface area is probably just the concentrator width * field length.

To estimate the instantaneous heat transfer rate from fluid to sky/ambient air, an iterative process is used to arrive at intermediate temps for the heat transfer path nodes the provide a heat transfer rate equilibrium along the path between nodes.  The path is divided into three sections: fluid to tube wall, tube wall to concentrator surface, and concentrator surface to sky/atmosphere.  The following manual calculation uses a mean value for the node temps. across time to arrive at a mean heat transfer rate to approximate the instantaneous heat transfer rate.  The mean temps. do not necessarily represent practical values and are unlikely to be accurate.  The calculation is mainly to illustrate the various relationships.  Below that, the system is modeled by computer to arrive at a reasonable accurate overall heat transfer using dynamic temps.

Fluid-to-wall:  Mean fluid temp. of 125°F = 325°K is chosen based on initial tank temp. of 180°F and final tank temp. of 70°F.  Heat transfer rate from the fluid in a 3/8" aluminum tube to the tube outer wall given the mean fluid temp., iteratively derived outer wall temp. of 117°F = 320.7°K, and estimated heat transfer coefficient of water for the low end of the laminar to turbulent transition, 750 W/(m°K) *, is [pi * (3/8) * 0.0254 m/in * 36 m concentrator length * 5 tube runs * (325°K - 320.7°K)] / [(1/750 W/(m²°K) water thermal conductivity) + (0.7 mm wall thickness / 250 W/(m°K) aluminum thermal conductivity)] = 17.3 kW.  With more turbulence, the heat transfer coefficient of water may increase by a factor of 50 or more *.

Wall-to-surface: Heat transfer from the tube outer wall to the concentrator surface is limited by the concentrator's cross-sectional area.  A likely concentrator material is sheet aluminum, with thickness of 1 mm, and conductivity of 250 W/(m°K).  The concentrator's parabolic circumference, when radius equals depth, is approximately 1.15 * 4 ft width = 4.6 ft.  The tube is looped into a number of  length-way runs on each concentrator section to raise the transfer capacity, with five runs selected from trial and error.  Given five runs equispaced along the parabolic circumference, an approximation for the wall-to-surface transfer rate is calculated by dividing the surface into 10 strips of 0.46 ft width.  Given that the temperature gradient causes more heat transfer from the surface nearer to the tube, the average conduction path length across a strip may be estimated at 25% of the strip width, or 0.1 ft.  The total concentrator length 30 ft/row * 4 rows = 120 ft.  The iteratively derived tube outer wall temp. is 117°F = 320.7°K and concentrator surface temp. is 107°F = 314.9 °K.  By Fourier's law the wall-to-surface transfer rate is 250 W/(m°K) * 1 mm thickness * 120 ft concentrator length * 5 tube runs * 2 strips/run * (320.7°K - 314.9°K)  / 0.1 ft = 17.4 kW.  Conduction through the frame should increase this value somewhat.

Surface-to-sky:A model for the radiative heat transfer rate from concentrator surface to sky may be derived from results of a University of Nebraska study (pdf) connecting sky emissivity to dewpoint and ambient air temperature:  The clear night sky emissivity, esky = 0.732 + 0.00635 * (dewpoint °C), and the effective sky temp. is Tsky°K = (esky * Tamb°K^4 )^0.25.  Given an arid climate mid-summer night mean dewpoint temp. 4 °C (40 °F), and mean ambient temp. 88 °F = 304 °K, then the U of N formula gives effective mean sky temp, Tsky°K = ((0.732 + 0.00635 * 4) * 304^4 )^0.25 = 283 °K = 50 °F.  The iteratively derived concentrator surface temp. is 107°F = 314.9 °K.  Given radiative surface area 43 m^2 (4 ft width * 4 rows * 30 ft row length occupying a 1000 sq. ft. roof area) and surface emissivity 0.95, the mean radiative surface-to-sky heat transfer rate during summer, using Stefan's law, is total transmissivity * Stefan's constant * surface area * ( Trad°K^4 - Tsky°K^4 ) = 0.95 * 5.67e-8 W/(m^2·K^4) * 43 m^2 *( 314.9^4 - 283^4 ) = 7.9 kW.

Surface-to-air: There is also a convection transfer from the concentrator surface to the ambient air:  Convective heat transfer coefficient for air ranges from 10 to 100 W/m²°K depending on wind speed/turbulence.  The concentrator's rear surface will point up and tend to get more airflow than the front surface which will point down.  The concentrator's supporting frame attached to the rear surface  will tend to create local air turbulence.  For these reasons the minimum transfer coefficient for the rear surface might be 15 W/m²°K with the front surface 5 W/m²°K, averaging to 10 W/m²°K.  Given an iteratively derived surface temp. of 107°F = 314.9 °K, a mean arid climate summer night ambient temp. 88 °F = 304 °K, a surface area of 2 * 43 m² = 86 m², the convection heat transfer rate is 10 W/m²°K * 86 m² * (314.9°K - 304°K) = 9.4 kW.  So for an arid climate calm summer night with clear sky, and dewpoint temp. 4 °C, the total surface-to-environment transfer rate would be about 7.9 kW + 9.4 kW = 17.3 kW. 

So the fluid-to-wall, wall-to-surface, and surface-to-environment transfer rates reach equilibrium at 17.3 kW.  In summer mid latitude there is around 10 hours between sunset/sunrise * so the total heat transfer is 173 kWh.  Humidity significantly lowers the cooling rate.  Wind significantly raises the cooling rate.  More fluid turbulence in the tube should improve overall transfer considerably.  Radiative transfer is probably higher than given, since the U of N sky emissivity calculation is based on a frequency range of greater atmospheric absorption compared to the relatively narrow frequency range of the STC's night sky cooling (3).  The cooling period may also be extended longer than 10 hours but with a lower transfer capacity.

An iterative computer program listed here models the continuously changing temp. and transfer rate gradients across the concentrator perpendicular to the tube and calculates the heat transfer rate.  The model assumes a constant fluid temp. along the tube and returns about 15.8 kW mean transfer rate for the above example.  Another iterative program listed here calls the first program and models the total heat transferred from the hot tank, accounting for the temp. drop along the tube and in the tank over time. The model reveals that the flow rate greatly influences the total heat transfer by its effect on the fluid temp. drop along the tube.  The model parameterized with a 1600 gal tank, four paralleled 120 gal/hr. flows (one per concentrator field row), starting temp. of 140°F and ending temp. of 93°F transfers the 185 kWh in ten hours.  These starting/ending temps are crudely estimated based on the condenser steam temp. of 250°F, an absorption cooler target COP of 0.7, and a reasonably insulated hot tank. 

The amount of aluminum tubing in this example, 600 ft., is a significant amount of material, but is necessary to compensate for the limited conductivity of the concentrator sheet aluminum.  One way to reduce the length of tubing is to attach sheet aluminum fins to the bottom of the concentrator, to also serve as structural support. 

A forced-air heat exchanger operating during the steam-making period is an alternative to night sky cooling that uses less material and space, with disadvantages that include fan energy draw and noise, and heating of the local microclimate.  The heat exchanger requires an electric fan, because a fan mounted on the turbine axle would present an unacceptable load during the winter.  The forced-air heat exchanger may be connected to the hot bank to reduce the number of heat exchangers in the condenser.  Forced-air heat exchangers for the absorption coolers might be optimum but probably not for the steam condenser given that the condenser heat exchange surface area (i.e. turbine backpressure) has to be minimized in the interest of efficiency.  The fans may be of the boundary layer type and the motors may be VFD-driven for load management.  The radiators may be coiled tubing around the perimeters of the fans for simple fabrication.

(1) Eliminating excess heat to the air during the day when air temp. is in the range 90°F to 115°F in the summer is relatively inefficient due to a poor temp. differential.  Winter day air provides a higher differential but remains a less efficient heatsink than the night sky given the STC's radiative ability. 
(2) See: * (pdf), * (pdf), *
(3) If the heat to be emitted is in the temp. range 70°F to 160°F, the range of peak wavelength is, by Wien's displacement law, 8.4 um to 10 um.  This wavelength range is shown to have an atmospheric transmittance range of about 60% to 90% *,*,*.  Increased atmospheric transmittance corresponds to increased radiative heat transfer because the high altitude atmospheric temp. is colder than the low altitude atmospheric temp.

Global Warming - nice atmospheric energy balance diagrams
A study of a polymer-based radiative cooling system (pdf)
Theoretical Evaluation of the NightCool Nocturnal Radiation Cooling Concept (pdf)


The STC's various thermal components, including pipes and tanks, require good insulation against radiation, conduction and convection heat loss/gain.  Heat loss/gain between objects is proportional to the exposed surface areas, various orders of the temperature differentials, and the objects' surface emissivity and internal conductivity coefficients which depend on material characteristics.  Radiation occurs with the air, nearby masses such as walls and the ground, and the sun/sky outdoors, and is usually the greater heat loss/gain mechanism (see molecular model).  Conduction occurs with nearby air and through support bodies but is usually a lesser mechanism.  Local air convection is usually modest but wind convection may easily surpass radiation as the greater loss/gain mechanism. Indoors, thermal component loss/gain can increase space heating/cooling loads.  Heat loss/gain usually compromises but occasionally enhances thermal efficiency of a system.

Component external surfaces should be painted to resist both corrosion and radiation loss/gain.  White titanium dioxide pigment reflects visible light well, protecting cold components located outdoors from the bulk of solar radiation.  Since white readily emits/absorbs infrared radiation, cold components may benefit further through heat loss to the night sky.  Silver (or aluminum) pigment provides the best infrared (actually full-spectrum) radiation reflection for hot components near heat sinks or cold components near heat sources.  The paint should withstand the component's temperature fluctuations for the life of the system.  Solvent(VOC)-free paint is best used.  The pigments might be obtained as powders and mixed with suitable binders to avoid the environmental hazards of commercial additives. 

To prepare the surface for paint, first, sharp edges and imperfections are ground smooth to prevent the paint from drawing thin.  Then oil is removed with mineral turpentine, and the surface is sanded or wire brushed to remove oxide (1) and polished quickly.  Immediately the surface is washed with detergent and pure water, rinsed well, and immediately dried under conditions of low ambient humidity, and low ambient temperature relative to the component temperature, which helps to dry it.  Immediately after drying, the surface is wiped with a tack cloth, and the first coat of paint is applied and cured.  Next, this layer is wiped with a tack cloth and a second coat is immediately applied and cured.  Then the paint is polished and the excess polish removed with a clean cloth.  The surface should remain clean.  For corrosion-prone metal, the coats should be thick. 

Given emissivity of 0.3 to 0.4 for metalized paint, an alternative is to coat the component with anti-corrosion paint, and cover it with aluminum foil using an adhesive to prevent the entrapment of corrosives behind the foil.  Aluminum foil has emissivity of 0.03 polished, about 0.15 oxidized, and as high as 0.4 when very dirty.  The total emissivity of two layers of oxidized foil is 0.15 * 0.15 = 0.023.  A clear dielectric coating is effective in preserving metal reflectivity, but is ineffective in preserving metal emissivity because the coating conducts and emits heat.  The shiny side should face the air space.

The component may then be enclosed in a thick blanket containing a large amount of anti-convection material, for example cellulose, perlite, cotton, wool, or straw.  Perlite withstands much higher temperatures.  Cellulose can be made from newspaper or straw with a fine paper shredder.  Straw can be harvested from most any dry grass.  Straw, wool and cotton can be bought from farmers.  Perlite is available in large bags from plant nursery supply. 

The thermal resistance per unit area of anti-convection material is described by its R-value,
the ratio of temperature differential to heat transfer rate.  R-value (SI) = °C*m²/W = 5.67446*R-value (US) = °F*ft²*h/Btu.  The R-values (US) at 75°F of perlite and straw are usually around R-3 per inch thickness and cellulose, cotton and wool around R-3.5.  For example, the loss rate through 1 ft² of cellulose, 2" thick, and temperature differential of 100 °F, is 100/(2*3.5)=14 Btu/h = 4.1 W.  R-values typically decrease 30% at 3x higher density so the material should remain uncompressed.  R-values typically decrease/increase 20% as temperatures increase/decrease 100°F .  A rough guideline for the optimum blanket thickness ratio for top : side : bottom is 5:3:1 for hot components and 1:3:5 for cold components but a true optimum has many dependencies. 

The anti-convection blanket should be separated from the component by an air gap of 0.5".  This reduces heat conduction between the solids and helps keep moisture/debris off the component.  Convection is minimum at this gap width.  The blanket's inner wall may be a thick aluminum foil separated from the component with spacers.  This foil supplies additional radiation reflection.  For pipes, the spacers can be wood donuts. With radiation and convection reduced as such, conduction through the various layers becomes a proportionally greater heat loss/gain mechanism.  Another air gap between the foil and blanket reduces conduction between them.  

The blanket should be enclosed in an aluminum outer shell to provide a third radiation reflection layer and to keep out water and debris, with the strength to resist pest intrusion, mechanical accidents, and an occasional cleaning.  An air gap between the blanket and outer shell would further reduce conduction. 

If the outer shell can be sealed then it may be filled with argon gas to reduce convection further. Sealing also eliminates water and vapor entry but there will likely be a gradual leakage so periodic gas recharge is probably required.  More practical than gas fill would be small drainage/ventilation holes in the aluminum layers.  Moisture degrades the thermal resistance of anti-convection materials and wreaks general mayhem with the various materials. Condensation on cold component surfaces can be a problem in humid environments, greatly accelerating
coating deterioration.  Air gaps in the anti-convection blanket should be carefully closed to prevent warm moist air flows to cold component surfaces, to minimize condensation risk.

The outer shell should be separated from surrounding objects by an air gap of 0.5".  Components should be located where the temperature of surrounding objects and air are closest to the component temperature.  Airflow should be minimal.

For galvanized surfaces, consult manufacturer about removing chemical treatments by abrasion, and abrasion limits to prevent damage.  More here.

Overall Heat Transfer formulas
Making Decisions with Insulation
Perlite Block and Cavity Fill
Preventing Corrosion Under Insulation
Thermal Resistance of Building Insulation

Control/Monitor Subsystem

The STC's digital control/monitor subsystem maintains the steam subsystem operation, the solar tracking function, the battery charge control, and thermal subsystems regulation.  The control/monitor subsystem maintains stability throughout the subsystems to minimizes stresses, maximize the life of the system and maximize efficiencies and energy availability with strategies based on energy usage patterns.  An important element of this task is handling failure modes to prevent/limit damage to components.  The availability of low-cost digital hardware to enable these functions contributes significantly to the feasibility of small scale solar thermal energy systems.

As a general-purpose computer, the control/monitor subsystem can function as an oscilloscope and other tools during development.  It can also monitor the system for failure modes after it is up and running.  Various acoustic transducers may be used to monitor/predict material stress and failures.  Data may be stored and gathered on maintenance calls.

The control/monitor subsystem may be implemented on a laptop computer or a system-on-a-board running the GNU/Linux operating system.  A non-proprietary operating system and computer architecture are preferable for access to documentation and ease of maintenance.   The computer should possess low-power capability.  A higher-power computer might run at a lower power and switch to full power when needed, for example, to perform cloud monitoring through an image sensor.  Control/monitor transducers interface through an expansion card. 

Simputer runs embedded GNU/Linux and may draw as little as 10 Wh per day.  Axis ETRAX is a system on a chip with full support by embedded GNU/Linux.  There is uClinux for microcontrollers.  Another possibility is the OpenRISC 1000 architecture with a GNU/Linux port and running on one of the FPGA-based prototype boards at Opencores.

This system-on-a-board would communicate with a GNU/Linux laptop computer through an infrared link.  The cost of these systems might be as low as $50.  Omitting signal-processing capability may make it as low as $10.  This does not include the interface electronics.  See electronics design/fab resources.  An FPGA-based processor implementation may also house glue logic for functions including multiple analog/digital input/output channels using a single D/A converter.

The laptop's advantage is that it simplifies software development.  The laptop has to meet the system lifespan.  If the control/monitor subsystem fails, damage might be done to the rest of the STC.  An analysis should be performed to determine what may be done to minimize damage in the event of such failure.  

Climate control is needed to limit heat buildup in the control/monitor subsystem and preserve the integrity of the plug-in connectors.  The control/monitor subsystem should be powered directly by the main storage batteries and be tolerant of a wide supply voltage range, transients and noise.

An introduction to open-source hardware development

Component Interactions

The turbine, generator, and condenser are in close proximity and heat transfer between these components should be minimized.   Heat loss from the turbine and the condenser top should be avoided while heat gain to the generator and the condenser reservoir should be avoided.  Heat transfer between components depends on the cross-sectional contact area.  Convection transfer depends on the component insulation and turbulence in the plant enclosure air.  Radiation transfer depends on the surface area and emissivity of the components. 

If the generator draws more heat from the turbine through the shaft, it may produce and benefit from a net heat loss through its housing to the plant enclosure structure and air, otherwise the generator housing should be insulated.  Ventilation for the plant enclosure should maintain an ambient temperature that balances heat loss and heat stress.

Energy Flow

Solar insolation and collector area/losses determine solar energy to the receiver.  Receiver temp. drop / friction loss and heat losses determine steam energy to turbine nozzle, given adequate flow rate.  Turbine temp. drop plus losses determine nozzle steam energy to shaft work.  Condenser temp. drop plus losses determine condenser heat to thermal apps, given adequate flow rate.  In the wider system there are also generator, battery, thermal bank and absorption cooler losses, plus pumping costs.

Flow rate example:  The prototypical STC system produces a maximum 343 kWh * 0.9 * 0.75 = 231 kWh of steam daily in Sch 40 3/4" carbon steel pipe rated at 250 psi working pressure and 400°F working temperature.  What is the average steam mass flow rate, volume flow rate, and turbine nozzle area that delivers this energy in 12 hours?  

From steam tables, steam enthalpy is 1200 btu/lb & specific volume is 1.85 ft³/lb.  Total energy to transfer is 231 kWh = 788500 btu, so total pounds is 788500/1200 = 657 lb.  Average mass flow rate is 657/(12hr*3600) = 0.015 lb/s = 6.9 g/s,  and average volume flow rate is 1.85 ft³/lb * 0.015 lb/s = 0.028 ft³/s = 0.0085 m³/s.  Nozzle area = volume flow rate / sonic velocity = 0.0085 (m³/s) / 400 (m/s) = 2.125e-5 m² = 0.212 cm² => circular diameter = 2*sqrt(0.212/π) = 0.47 cm.  Average steam velocity in 3/4" pipe = 0.0085 (m³/s) / ( (0.75²*π/4)(in²)* 0.0006452 (m²/in²)) = 30 m/s.  Peak steam velocity during the middle of the day is substantially higher.  See Friction Loss.

If the section of pipe containing water is Sch 40 1/2" carbon steel pipe, and the other parameters are same as above, what is the  average volume flow rate and velocity of the water?   Volume flow rate = mass flow rate / density of water = 6.9 g/s / 950 kg/m³ = 0.727e-5 m³/s = 2.57e-4  f³/s = 0.12 gal/min.  Velocity = (2.57e-4  ft³/s)/((0.5/12)² ft² * π/4) = 0.19 ft/s = 0.058 m/s.

According to [1], 0.058 m/s through a 1/2" Sch 40 pipe has a Reynolds number of 811 which indicates laminar flow (under 2300).  According to [2], typical water heat transfer coefficient ranges from 500 to 10 000 W/(m²K) so the heat transfer coefficient for Reynolds number 811 and 0.058 m/s is probably around 500 W/(m²K).

[1] Reynolds Number
[2] Overall Heat Transfer Coefficient

The Rankine Cycle heat engine converts heat energy into mechanical work using water/steam as the working fluid.
rankine cycle

More on Rankine Cycle
Energy Conversion Ebook - Weston
Ch2 Fundamentals of Steam Power (pdf)
Ch9 Advanced Systems - Cogeneration (pdf)


The thermal efficiency of a heat engine is defined as W/Qh = 1 - Qc/Qh, where W = mechanical work out, Qh is the heat transferred from the hot reservoir to the engine, and Qc is the heat transferred from the engine to the cold reservoirCarnot's theorem states that the heat engine's theoretical maximum thermal efficiency (Carnot efficiency) is 1 - Tc/Th, with Th = absolute temp. of the hot reservoir and Tc = absolute temp. of the cold reservoir.  In a molecular interpretation of the theorem, the average working fluid molecule can give up to mechanical work at most the difference between its thermal energy while at the hot reservior temp. and its thermal energy while at the cold reservoir temp. 

For the STC's Rankine cycle, Carnot's theorem means that the higher the receiver pipe temp. (Th), and the lower the condenser coolant pipe temp. (Tc), the higher the theoretical maximum of the conversion efficiency from solar energy (Qh) to turbine shaft work (W).  The Carnot efficiency (i.e. Th, and Th - Tc) is chosen to balance material quantity/quality for minimum cost.  At lower Carnot efficiency (lower Th and Th - Tc) the quantity of materials increases and at higher Carnot efficiency the quality of materials increases, generally.

In terms of the heat engine's thermal efficiency, the overall solar to electrical conversion efficiency is the product of the thermal efficiency (product of the Carnot efficiency and solar to mechanical conversion efficiencies) and the mechanical to electrical conversion efficiencies.  In simper terms, the overall solar to electrical conversion efficiency is the product of the Carnot efficiency and all solar to electrical conversion efficiencies.  The conversion efficiencies are determined by the energy losses in the various system components.  Listed below are the target efficiencies of individual elements in the solar to electrical conversion.

Target Efficiencies
Solar to Electrical Conversion
Target Efficiencies
receiver 0.85
turbine 0.40
inverter 0.95

Overall Solar to Electrical Conversion Target Efficiency

The effective hot and cold reservoir temps. that determine the system's Carnot efficiency are mainly a function of the climate, season, choice between night sky cooling and daytime forced air cooling, and choice of steam temp.  Using night sky cooling in a mid-latitude arid climate, the cold reservoir average temp., Tc =  40F in winter and

Prototypical System Capacities

Given a mid-latitude arid climate winter minimum day radiation of 138 kWh/day for a 1000 sq. ft. concentrator field with 4 ft wide concentrators, available electrical energy to end-use is 138 kWh/day * 0.18 = 25 kWh/day.  Available thermal energy to end-use is 138 kWh/day * 0.90 * 0.75 * (1 - 0.40) = 56 kWh/day.

Given a mid-latitude arid climate summer maximum day radiation of 343 kWh/day for a 1000 sq. ft. concentrator field with 4 ft wide concentrators, available electrical energy to end-use is 343 kWh/day * 0.18  = 62 kWh/day.  Available thermal energy to end-use is 343 kWh/day * 0.90 * 0.75 * (1 - 0.40) = 139 kWh/day.

Heat Exchangers

A heat exchanger is a device that exchanges heat between two fluids separated by a solid wall.  Since heat transfer is proportional to the surface area of the wall, designs tend to maximize the surface area.  In the shell and tube type heat exchanger, one fluid circulates inside a bundle of tubes while the other flows on the outside surfaces of the tube bundle and is enclosed in a shell.  To the extent that the fluid flows are parallel, the most efficient heat transfer occurs when the flows are in opposite directions, called counter-flow.  This is due to a higher average temperature differential across the length of the heat exchanger.

In applications involving high temperature/pressure fluids, the tubing is straight and made from carbon steel or higher grade steel.  For lower temperature/pressure, the tubing is made from copper or aluminum for high thermal conductivity, and may be coiled to create turbulence inside, which aids heat transfer between the fluid and the tube wallTurbulence increases with a smaller radius coil but the minimum is limited by bending stress.  Turbulence also increases with fluid velocity, which tends to increase with smaller tube diameters.  The increased heat transfer by turbulence must be balanced against the added stress on the tubing and the added load on the pump.

Thinner tube walls also increase
heat transfer but the trade-off is lower strength.  Tube diameter affects heat transfer through the ratio of surface area to fluid volume.  Decreasing tube diameter increases heat transfer, but this must be balanced against increased friction and pump load.  Multiple small tubes connected in parallel by use of a header on each end offers increased heat transfer over a single large tube by virtue of increased total surface area, but also increased friction and pump load.  Reliability decreases as the number of tube/header connections increases.  Heat transfer for the fluid outside the tubes is typically enhanced by baffles that direct most of the fluid flow onto the tubes and away from the outer shell, which should be well-insulated.

Higher fluid temperatures and temperature differentials also increase stress on the tubing.  Imperfections in the inside tubing surface are more vulnerable to stress and create local turbulence that causes even more stress, so all fluid contact surfaces should be clean, smooth and defect-free.  Corrosion caused by fluid impurities makes tubing more vulnerable to stress, so fluids should be pure.  An optimum coil bend radius and level of turbulence exists for a given set of temperatures and flowrates, tubing conductivity and thickness, and target system lifetime.

The heat transfer rate may be roughly modeled for an incremental section of the heat exchanger, given the characteristics of the solid wall and the fluids' convection heat transfer coefficients, which depend on fluid characteristics, flow rate and turbulence.  Accurate modeling of heat transfer rate for the entire heat exchanger must use the log-mean temperature difference derived from the four inlet/outlet fluid temperatures, since the fluid temperatures change as the fluids traverse the heat exchanger.  If the output temperatures are unavailable, the NTU method may be used.

More on Heat Exchangers · Plate heat exchanger · Spiral Heat Exchangers
Heat Transfer - Spirax Sarco
Heat Transfer Coefficients for some common Fluids and Heat Exchanger Surfaces
Helically Coiled Heat Exchangers Offer Advantages (pdf)
Wolverine Heat Transfer Data Book II (pdf)
DOE Fundamentals Handbooks : Thermodynamics, Heat Transfer, and Fluid Flow vol 1 vol 2 vol 3 (pdf)

Image Absorption Cooler Diagram

Locating the Thermal Banks
The thermal banks' locations can significantly affect heat loss/gain to the environment.  Given Ta = average ambient temperature (°F), and Tb = hot bank temperature (°F) at summer/winter dusk/dawn, select A.) housing the hot bank inside or outside the temperature-regulated residential space, B.) exposing or not exposing to wind, C.) exposing or not exposing to the vertical sky (summer sun/sky radiation exchange), D.) exposing or not exposing to the low equator sky (winter sun/sky radiation exchange), and E.) exposing or not exposing to nearby massive objects (infrared heat exchange).
              Ta   Tb     inside   wind   vertical  equator  objects

summer dusk 100 185 no ok no ok ok

summer dawn 70 45 ok no ok ok no

winter dusk 70 145 ok no no ok no

winter dawn 45 40 no ok ok ok ok

This suggests the hot bank should be placed outside the residential structure, protected from the wind, protected from the vertical sky, protected from nearby massive objects, but may be exposed to the low equator sky.  This calls for an enclosed shed, outside the residential structure, with a window facing the equator.  The equator side happens to be the ideal location on the roof for the STC's main plant, so pipes may be kept short.  The shed floor should be well-drained to handle a major tank leak.  An overhang would protect the window from summer sun, and probably an open vent in summer would help. 

Given cold bank temperatures of 45°F at dusk, 75°F at dawn in summer, and not used in winter, it could be kept inside nearer the refrigerator, protected from nearby massive objects. 

Tank and Cooling Options

 Option 1
 Option 2 Option 3
tank size
large medium small
night sky cooling
C -
forced-air cooling - A
material costs
energy costs
environ. costs
low moderate
C = steam condenser waste heat
A = absorption coolers waste heat

600/700 gal Hot Bank Example (see Prototypical STC system)

In the arrangement below the 600 gal. tank maintains a minimum 140°F temp. round-clock for tap water heating and is sized to meet summer/winter heat storage requirements.  The fridge absorption cooler is operated first each morning while the 600 gal. tank temp. is near its minimum 140°F, after which the condenser raises the tank temp. to 180°F to meet summer/winter heat storage requirements.  By cooling the fridge absorption cooler with the 600 gal. tank, fridge waste heat supplies tap water heating year-round and also supplements space heating in the winter.  A separate 700 gal. tank is needed to cool the space absorption cooler which places an upper limit of 140°F on the tank temp.  The 700 gal. tank is cooled at night by night sky cooling with no minimum temp. restriction. 

Thermal Applications Diagram Image


Copyright (c) 2005-2009 Robert Drury
Permission is granted to copy, distribute and/or modify this document
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with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
See "GNU Free Documentation License". 

Disclaimer:  This information may contain inaccuracies and is provided
without warranty.  Safety first when working with high temperatures,
pressures, potentials, speeds, energies, various tools and materials.