Trilateral Flash Cycle Research Articles

Multi-aspect assessment and optimization of a poly-generation layout composed of a geothermal power plant and a wind turbine

The current research is an effort to propose a novel poly-generation layout by hybridization of wind power and geothermal energy as two renewable heat sources. The geothermal unit comprises a steam flash cycle as the topping system and a Kalina flash cycle as the bottoming system. Hot water is produced through the utilization of the energy of the geothermal water before reinjection to the ground. An E126/7580 wind turbine is accountable for generating the favorable output electricity. Moreover, the waste heat from the generator of the wind turbine is recovered in a trilateral flash cycle. The sum of power produced by the steam flash cycle and the trilateral flash cycle is employed to generate hydrogen in an electrolysis unit. Moreover, the output electricity of the Kalina flash cycle is employed to produce cooling and freshwater in a transcritical CO2 refrigeration cycle and a reverse osmosis desalination system. The final evaluation of the system utilizing energy and exergy-economic analyses and three-objective optimization of the layout revealed an exergetic efficiency of 37.11 % in the optimum case. The configuration produces 771.7 kW, 454.3 kW, 3585 kW, 1.29 kgh-1, and 3 kgs-1 of electricity, cooling, heating, hydrogen, and freshwater, correspondingly. The economic analysis of the system indicates a total cost rate of 140.2 $h-1, a specific cost of products equal to 19.5 $GJ-1, and a payback period of 1.03 years, suggesting an excellent economic performance for such a complex system.

Exploring performance map: theoretical analysis of subcritical and transcritical power cycles with wet and isentropic working fluids

This study examines the overall thermodynamic efficiency of several power cycles, including transcritical power cycle (TPC), trilateral flash cycle, organic Rankine cycle (ORC), partially evaporated ORC, and superheated ORC under both ideal and specific conditions. The research focuses on specific wet and isentropic working fluids, providing a performance map of the power system with identical configurations, internal machine efficiency, and vapor quality. Moreover, this study aims to determine the ideal working fluid to utilize given heat sources by TPC. The results indicate that the efficiency of TPC may reach a maximum and subsequently decrease under certain conditions. Moreover, some operating conditions for the thermal power system, such as temperature range and configurations, may not be recommended due to exceptionally low or negative effective thermodynamic cycle efficiencies. Furthermore, the study demonstrates that increasing the inlet temperature of the working fluid to an expander does not necessarily lead to higher power cycle efficiency, as observed in the case of TPC. However, the result also proves the potential of carbon dioxide (R744) as a promising working fluid when chosen for a TPC with x2,is = 1.00, still achieving positive effective efficiency under specific conditions.

Thermal efficiency investigation for organic Rankine cycle and trilateral flash cycle using hydrofluoroether working fluids

The thermal efficiency of the organic Rankine cycle (ORC) is higher than the trilateral flash cycle (TFC) using normal dry working fluids. On the contrary, the thermal efficiency of TFC outperforms the thermal efficiency of ORC by using super dry working fluids at specific conditions. This study aims to investigate thermal efficiency for TFC and ORC cycles using HFE7100 and HFE7500, classified as super dry working fluids. The effect of two techniques was studied on the thermal efficiency of ORC and TFC: the recuperator cycle (RORC and RTFC) with various ratios of effectiveness and the partial evaporator organic Rankine cycle (PE-ORC), with various ratios of vapor quality. The results indicated that the recuperative heat exchanger helps convert the super dry behavior to be like normal dry. Therefore, using HFE7100 required 0.2 effectiveness of recuperative heat exchanger, while for HFE7500, 0.4 effectiveness is needed. A partial evaporator cannot help convert the super dry's behavior to the normal dry fluid completely, while it has the crucial role of moving the intersection point towards critical temperatures (Tcr), which increases the range of heat source temperatures that assist super dry fluids to behave as normal dry fluids. However, PE-ORC can be a good competitor to TFC at vapor quality (x = 0.1, and x = 0.2) and (x = 0.1), and it has higher thermal efficiency than ORC at vapor quality (x = 0.9) and (x = 0.8 and x = 0.9) for HFE7100, and HFE7500 respectively.

Techno-economic and 4E comparisons of various thermodynamic power cycles for low-medium grade heat recovery

Various thermodynamic power cycles can be utilized to convert the low-to-medium temperature heat (available from many sources and has huge potential) to electricity and a detailed comparison between all of them is essential to identify the suitable one. Hence, to fulfill this research gap, six thermodynamic power cycles (Organic Rankine cycle with dry fluid, Organic Rankine cycle with wet fluid, Transcritical CO2 Rankine cycle, Kalina cycle, Organic flash cycle and Trilateral flash cycle) have been compared for various heat source and sink temperatures. Objective functions are power generation, efficiency, irreversibility, cost, profit, environmental benefit, techno-economic parameters, etc. Study shows that the trilateral flash cycle is best for medium heat source temperature and the CO2 cycle is best for low heat source temperature. The trilateral flash cycle shows an 11.5% higher exergy efficiency and 16.16% increment in annual profit at 160 °C heat source temperature as compared to the organic Rankine cycle with dry fluid. A decrease in condenser temperature is more advantageous than an increase. The study reveals that the CO2 Rankine cycle would be advantageous for low-grade heat sources while the trilateral flash cycle for medium-grade heat sources in terms of performance, cost, design, operation and environmental benefits.

Assessment of the Trilateral Flash Cycle potential for efficient solar energy conversion in Europe

The potential of the Trilateral Flash Cycle (TFC) for the efficient conversion of solar energy to power in Europe is assessed in this work. A numerical analysis of a Solar-TFC thermal power unit is performed, by applying an in-house numerical model. Flat Plate Collectors (FPC) and Evacuated Tube Collectors (ETC) are modeled as solar heat sources. Particular focus is on the technological bottleneck of the TFC, i.e. two-phase expansion, by applying a novel two-phase expansion numerical model. Annual simulations are performed with the total efficiency of the Solar-TFC maximized at each time step. The annual total efficiency of the Solar-TFC, exergy efficiency, and thermal efficiency of the TFC can be as high as 5%, 5.3%, and 11%, respectively. ETCs increase the economic viability of the Solar-TFC, particularly as the annual electricity output increases. The Levelized Cost of Electricity (LCOE) of the modeled unit is estimated in the range of 0.25 and 0.75 €/kWh, which can be further reduced by increasing the collectors’ area. The Solar-TFC unit can reduce, on an annual basis, the CO2 emissions by 2.5–47 kg per m2 of solar collectors, with the carbon footprint reduction depending on the collectors’ efficiency and the installation location.

Numerical study of the flow in a two-phase nozzle for trilateral flash cycle applications

A two-phase nozzle is a critical component in organic flash systems, and its design and operation must be carefully considered to handle the complex two-phase flow of the working fluid and achieve system performance. This study deals with the use of computational fluid dynamics (CFD) to assess the performance of a converging–diverging nozzle in a trilateral flash cycle (TFC) system. Simulations have been performed using available cavitation models and the turbulence closure is achieved using the Realizable k-ε model. In particular, the flow features in terms of the generated thrust, the pressure distribution, velocity, and void fraction within the two-phase nozzle have been calculated with isopentane as the working medium for inlet temperatures of 50 °C and 60 °C. Two cavitation models, namely the Schnerr and Sauer model and the Zwart-Gerber-Belamri have been selected and their results have been compared to experimental measurements from the literature. It is observed that the thrust force improves as the working fluid inlet temperature rises. Results in terms of the static pressure, velocity, and void fraction are consistent with the physics of flashing flows in two-phase nozzles. Indeed, the static pressure and velocity remain almost constant after the throat. Furthermore, the flow leaving the nozzle is predominately vaporized. The numerical model could be used to perform a parametric study to examine the effect of various parameters, such as nozzle geometry, inlet conditions, and thermodynamic properties of the working fluid, on the nozzle performance and identify the optimal operating conditions.

Effect of the working fluids critical temperature on thermal performance for trilateral flash cycle and organic Rankine cycle

The critical temperature (Tcr) is one of the important thermophysical properties of the working fluid, and it has a crucial effect on the output parameters of thermodynamic cycles used for power generation. This study aims to show the effect of the working fluids Tcr on the cycle thermal performance (thermal efficiency (ηth) and net-work output (Wnet) at the same heat source/heat sink temperature. For this purpose, 13 alkanes and 10 halogenated alkanes working fluids were investigated. Two different kinds of subcritical cycles, namely the Organic Rankine Cycle (ORC) and Trilateral Flash Cycle (TFC), were investigated. Pure and mixed (with various compositions) working fluids were used. Finally, it has been shown that although the critical temperature is an important factor, it can be correlated with output parameters only by using chemically similar working fluids.

Investigation of thermal efficiency for subcritical ORC and TFC using super dry working fluids

AbstractEfficiency is a crucial factor for power cycles. Generally, in the same temperature range, the cycle efficiency for a basic organic Rankine cycle (ORC) is higher than a similar trilateral flash cycle (TFC) for almost all working fluids and heat source/heat sink temperature pairs. According to some recent results, by using super dry working fluids, the thermal efficiency of TFC can outperform its ORC counterpart at high temperatures. This study performed the thermodynamics analysis using three dry working fluids with subcritical basic ORC and TFC with zero to partial recuperated heat ratio. The results showed that using recuperative heat exchange effectively contributes to increasing the efficiency of ORC and TFC. However, the rate of efficiency increase in ORC is higher than the TFC, which can be clearly seen, especially at high maximal cycle temperatures. Using super dry working fluids, the recuperator‐free TFC has favorable cycle efficiency at high heat source temperatures. In contrast, by adding heat recovery for both systems, the ORC can outperform the TFC at 0.4, 0.2, and 0.1 recuperated heat effectiveness for Dodecane, Decane, and Nonane, respectively.

Assessment of the thermal efficiency of subcritical power generation cycles using environmentally friendly fluids at various heat source temperatures

AbstractThis study aims to investigate the effect of the various heat source temperature (Tmax) on thermal efficiency (ηth) for the organic rankine cycle (ORC), trilateral flash cycle (TFC), and partial evaporator (PE‐ORC). For this purpose, HFE7000, HFE7100, and HFE7500 were used as working fluids (WFs). The results indicate that by using HFE7000, the maximum ηth was obtained for all used power cycles and temperature ranges. Compared to HFE7100, HFE7500 has higher ηth at TFC, and PE‐ORC at low Tmax, while HFE7100 has the maximum value at high Tmax. The ηth at Tmax = 353 K for TFC were 8.71%, 8.34%, and 8.59%, while for ORC 12.38%, 11.82%, and 11.71% for HFE7000, HFE7100, and HFE7500, respectively. At Tmax = 423 K for TFC were 17.65%, 16.26%, and 16.52%, while for ORC were 18.56%, 17.38%, and 16.59% for HFE7000, HFE7100, and HFE7500, respectively. The ηth results indicate that the maximum improvement at TFC by using HFE7000, and the minimum was at HFE7100, while for ORC, the maximum was at HFE7000, and the minimum was at HFE7500. Therefore, the HFE7000 fluid behaves as normal dry fluids at any used temperature, while HFE7100 as normal dry WFs at low Tmax while behaving as very dry WFs at Tmax extremely close to its Tcr. HFE7500 behaves as very dry working fluids. The ηth intersections temperature was at Tmax = 425.2 K and Tmax = 455.9 K for HFE7500 and HFE7100, respectively. However, there is no ηth intersection for HFE7000.

A Comparative Study of Cooling Sources in Organic Rankine Cycle for Low-Temperature Geothermal Heat Sources

Geothermal energy refers to ground heat sources exploited for many purposes (for example, generating electricity). A steam power plant, that uses water as a medium and operating on the Rankine cycle, is a prospective technology that can be used to generate electricity utilizing geothermal heat. However, due to the thermal properties of the applied working fluid, the steam power plant has the limitation that may not utilize cold source like liquefied dimethyl ether (DME) at the temperature of around -25 °C or the extreme one, like liquefied natural gas (LNG) at the temperature of around -160 °C. For this reason, it seems that RC using an organic working fluid (so-called ORC) is an appropriate technology to utilize heat sources of extremely low temperatures. Selected ORC working fluids are considered suitable to absorb the cold source. This paper reported the thermodynamic modelling analysis and a comparison of geothermal power systems exploiting air, water, LNG, and DME as the cooling medium of the ORC. The simple scheme of ORC is used for modelling, furthermore, the Trilateral Flash Cycle (TFC) is described as a comparative study. Thanks to the LNG technology, it is already mature enough, and the method of altering the phase into liquefied form is likely to store the energy (i.e., the power to liquid). In the liquefied form, natural gas can be easily distributed and transported at a certain distance. In this model system, the result shows that LNG and DME appear to be excellent options for increasing the operating range of ORC. The modelling result shows that combining propane (a working fluid inside the cycle) and LNG (a cooling source) has a wider operating range and is a good option to exploit low-temperature geothermal heat as a power generation system. Also, using DME for both cooling sources and the working fluid inside the geothermal power system employing ORC outperforms other ones. Taking advantage of using them as a cooling source is significantly boosting the potential deriving from low-temperature geothermal energy (i.e., below 90 °C) as promising sources in the future.

Multi-objective optimisation of supercritical CO<SUB align=right>2 combined cycles based on energy-exergy-economy balanced analysis

In this paper, the supercritical CO2 (sCO2) recompression cycle combined cycles are analysed, where the bottom cycles include transcritical CO2 (tCO2), organic Rankine cycle (ORC) or trilateral flash cycle (TFC). The working fluid for the ORC and the TFC can be R123, R245fa, or n-Pentane. We implemented four sub-models in our calculation: 1) thermodynamic model; 2) heat transfer model; 3) economic model; 4) exergoeconomic model. The specific exergy costing (SPECO) method is utilised in the exergoeconomic model, and the multi-objective genetic algorithm is adopted to give the Pareto front of total unit exergy cost of the product (cPtot) and the thermal efficiency. Our model has been validated with the existing literature. The results show that the thermal efficiency standalone CO2 achieved 41.66% while attaching the tCO2, ORC, or TFC bottom cycle could improve the thermal efficiency by 1.1%, 1.68%, or 0.05%, respectively. In the meantime, the (cPtot, which is the representation of the cost, decreased by 0.2$/GJ for ORC and increased by 0.06$/GJ and 1.05$/GJ for tCO2 and TFC respectively. The influence of different working fluids for ORC and TFC is not obvious. Therefore, attaching the ORC as the bottom cycle will bring about the best performance and lowest cost.

Exergo-economic comparison of waste heat recovery cycles for a cement industry case study

This work evaluates the performance regarding exergo-economic and emissions requirements of Waste Heat Recovery configurations (Organic Rankine cycle, Trilateral flash cycle, and Kalina cycle) under different operating conditions and working fluids. It was found that the best economic performance is presented by the Organic Rankine cycle that operates with Cyclo-Pentane and has two intermediate heat exchangers since it pushes the expansion temperature up while allowing a higher heat input to the cycle. As a result, it delivers 6.2 MW with a net present value, the net present value of 0.74 million dollars, saving up to 11480 tonnes of carbon dioxide per year. This performance far exceeds that obtained in the previous work, around 50% higher net-work with 80% higher net present value, and constitutes the best alternative in terms of performance to recover waste heat from the source evaluated. Regarding the Trilateral flash cycle, it can be stated that the net work and the exergetic performance are independent of the working fluid as long as there is not a very large volume change in the expander. The Kalina cycle presents slight exergy destruction, but the power delivered does not compensate for the high total capital cost due to the high pressures that must be handled, 55–120 bar, compared to the Organic Rankine cycle, 4–40 bar. An approach was made to more realistic cases where the methodology used facilitates selecting the best alternative when there is a budget restriction using the total capital cost and net work alternatively like a fixed requirement and net present value as the primary decision criterion.

Thermodynamic efficiency of trilateral flash cycle, organic Rankine cycle and partially evaporated organic Rankine cycle

Emerging and promising ways of utilizing any heat sources from geothermal, solar, combustion, and industrial waste heat may be the application of power plants that are operating according to conventional Rankine cycle (RC), organic Rankine cycle (ORC), trilateral flash cycle (TFC) employing different types of expansion (i.e., volumetric expanders or turbine). In this paper, the studies about partially evaporated ORC (PE-ORC) was carried out; furthermore, it reports on novel results related to the comparison of thermodynamic efficiency of TFC, ORC and PE-ORC. These results were obtained by modelling the system operations computed with MATLAB and the thermal properties library taken from CoolProp and REFPROP. The calculation was based on selected different types of working fluid classified by A, C, Z, M, N points (conventionally categorized by dry, wet, and isentropic working fluids) and the upper-lower operating temperature. The obtained results explain a new point of view on the efficiency of TFC, ORC and PE-ORC plants, that in some of the conditions (i.e., one can find certain combinations of working fluid quality, maximal and minimal cycle temperature), the efficiency of PE-ORCs outperforms TFC and ORC. It means that at certain temperature ranges and conditions when starting the expansion step from a partially evaporated state, it may be recommended to improve the performance of the cycle. It seems that obtained results offer new insight to scientists and engineers in designing the thermal power plant working under a subcritical cycle with high-temperature heat sources or a low-temperature heat sinks employing the selection of working fluids and different types of expanders.

Effect of high temperatures on the efficiency of sub-critical CO2 cycle

AbstractThermodynamic efficiency is a crucial factor of a power cycle. Most of the studies indicated that efficiency increases with increasing heat source temperature, regardless of heat source type. Although this assumption generally is right, when the heat source temperature is close to the critical temperature, increasing the heat source temperature can decrease efficiency. Therefore, in some cases, the increase in the source temperature, like using improved or more collectors for a solar heat source can have a double negative effect by decreasing efficiency while increasing the installation costs. In this paper, a comparison of the CO2 subcritical cycle and the Trilateral Flash Cycle will be presented to show the potential negative effect of heat source temperature increase.

Using a Partially Evaporating Cycle to Improve the Volume Ratio Problem of the Trilateral Flash Cycle for Low-Grade Heat Recovery.

This study examined the trilateral flash cycle characteristics (TFC) and partially evaporating cycle (PEC) using a low-grade heat source at 80 °C. The evaporation temperature and mass flow rate of the working fluids and the expander inlet’s quality were optimized through pinch point observation. This can help advance methods in determining the best design points and their operating conditions. The results indicated the partially evaporating cycle could solve the high-volume ratio problem without sacrificing the net power and thermal efficiency performance. When the system operation’s saturation temperature decreased by 10 °C, the net power, thermal efficiency, and volume ratio of the trilateral flash cycle system decreased by approximately 20%. Conversely, with the same operational conditions, the net power and thermal efficiency of the partially evaporating cycle system decreased by only approximately 3%; however, the volume ratio decreased by more than 50%. When the system operating temperature was under 63 °C, each fluid’s volume ratio could decrease to approximately 5. The problem of high excessive expansion would be solved from the features of the partially evaporating cycle, and it will keep the ideal power generation efficiency and improve expander manufacturing.

Thermodynamic Efficiency Maximum of Simple Organic Rankine Cycles

The increase of the maximal cycle temperature is considered as one of the best tools to increase cycle efficiency for all thermodynamic cycles, including Organic Rankine Cycles (ORC). Technically, this can be done in various ways, but probably the best solution is the use of hybrid systems, i.e., using an added high-temperature heat source to the existing low-temperature heat source. Obviously, this kind of improvement has technical difficulties and added costs; therefore, the increase of efficiency by increasing the maximal temperature sometimes has technical and/or financial limits. In this paper, we would like to show that for an ideal, simple-layout ORC system, a thermodynamic efficiency-maximum can also exist. It means that for several working fluids, the thermodynamic efficiency vs. maximal cycle temperature function has a maximum, located in the sub-critical temperature range. A proof will be given by comparing ORC efficiencies with TFC (Trilateral Flash Cycle) efficiencies; for wet working fluids, further theoretical evidence can be given. The group of working fluids with this kind of maximum will be defined. Generalization for normal (steam) Rankine cycles and CO2 subcritical Rankine cycles will also be shown. Based on these results, one can conclude that the increase of the maximal cycle temperature is not always a useful tool for efficiency-increase; this result can be especially important for hybrid systems.

The effect of recuperator on the efficiency of ORC and TFC with very dry working fluid

Organic Rankine Cycles (ORC) and Trilateral Flash Cycles (TFC) are very similar power cycles; ideally, they have a reversible adiabatic (isentropic) compression, an isobaric heating, an isentropic expansion and an isobaric cooling. The main difference is that for ORC, the heating includes the full evaporation of the working fluid (prior expansion); therefore, the expansion starts in a saturated or dry vapour state, while for TFC, the heating terminates upon reaching the saturated liquid states. Therefore, for TFT, expansion liquid/vapour state (in bubbly liquid or in vapour dispersed with droplets), requiring a special two-phase expander. Being ORC a more “complete” cycle, one would expect that its thermodynamic efficiency is always higher than for a TFC, between the same temperatures and using the same working fluids. Surprisingly, it was shown that for very dry working fluids, the efficiency of TFC can exceed the efficiency of basic (i.e. recuperator- and superheater-free) ORC, choosing sufficiently high (but still subcritical) maximal cycle temperature. Therefore in these cases, TFC (having a simpler heat exchange unit for heating) can be a better choice than ORC. The presence of a recuperator can influence the situation; by recovering the proper percentage of the remaining heat (after the expansion), the efficiency of ORC can reach and even pass the efficiency of TFC.

The efficiency of transcritical CO2 cycle near critical point and with high temperature

Efficiency is a key parameter used to assess the quality of operation of power generation systems and devices applied for converting one type of energy to the other. Although, in the end, an investment project is mainly evaluated by economic aspect. Furthermore, many researchers have been investigating the possible types of energy conversion systems and devices applied for power generation and utilizing different types of working fluids. This paper presents the inside into transcritical carbon dioxide (CO2) cycle and the gradients of its efficiency. Transcritical CO2 cycle (TCO2C) here refers to a CO2-based thermal power generation cycle absorbing heat from a heat source (ideally with constant pressure) till the supercritical state is reached. It is followed by an expansion to a sub-critical superheated or even two-phase (wet) state. As alternatives, trilateral flash cycle (TFC) and organic Rankine cycle (ORC) utilizing CO2 are also introduced in this paper. The calculation in this study is computed based on MATLAB integrated with thermophysical properties like CoolProp and REFPROP, the mathematical models of the system are built and calculated with the same heat sink temperature of 224.41 K, and the heat source temperature is varied between 274.41 K and 500 K. At a certain temperature, the obtained result shows that the efficiency of the TCO2C is lower than the efficiency of ORC. Another result proves that the quality of working fluid at the end of the expansion process significantly influences the efficiency of the cycle.

Cold Energy Utilization in LNG Regasification System Using Organic Rankine Cycle and Trilateral Flash Cycle

"Cold energy" refers to a potential to generate power by utilizing the exergy of cryogenic systems, like Liquefied Natural Gas (LNG), using it as the cold side of a thermodynamic cycle, while the hot side can be even on the ambient temperature. For this purpose, the cryogenic Organic Rankine Cycle (ORC) is one type of promising solution with comprehensive benefits to generate electricity. The performance of this cycle depends on the applied working fluid. This paper focuses on the applicability of some natural working fluids and analyzes their performance upon cold energy utilization in the LNG regasification system. An alternative method, the cryogenic Trilateral Flash Cycle (TFC), is also presented here. The selection of working fluid is a multi-step process; the first step uses thermodynamic criteria, while the second one is addressing environmental and safety issues. It will be shown that in LNG regasification systems, single cryogenic ORC performs higher net output power and net efficiency compared to single cryogenic TFC. Propane as working fluid in the single cryogenic ORC generates the highest net output power and net efficiency. It is demonstrated, that concerning 26 novel LNG terminals, a net power output around 320 MW could be recovered from the cold energy by installing a simple cycle, namely a single-step cryogenic ORC unit using propane as working fluid.

Experimental investigation of nozzle geometry effect on two-phase nozzle performance through trilateral flash cycle

This paper aims to elucidate the effect of the divergent geometry of a nozzle on its performance by experimentally estimating the force generated by high speed two-phase fluid leaving the nozzle exit. The experiments are carried out by using the nozzles with two diverging profiles of conical and bell and various divergent angles of 6°, 18° and 30° corresponding to the divergent lengths of 45 mm, 17 mm and 12 mm respectively. The nozzles are examined at inlet temperatures of 50 °C and 60 °C for Isopentane as working fluid. The experimental results are indicative of higher values for thrust force and consequently isentropic efficiency by increasing the inlet temperature from 50 °C to 60 °C for all examined nozzles. It is found through the experiments that the maximum efficiency is about 41% with inlet temperature of 60 °C for the bell shape nozzle with the corresponding divergent angle of 6°. Whereas, the 30° conical and bell nozzles have the least force and efficiency. The pressure measurements along the 6° conical and bell nozzles are indicative of a greater pressure drop after the nozzle throat for bell shape nozzle compared to conical nozzle. This paper presents empirical results that can be used in designing efficient nozzles.