Abstract John D. 1, Graham L. Morrison 2 and Masud Behnia 3 1 Department of Engineering, Australian National University, ACT 2 Department of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 3 Dean of Graduate Studies, University of Sydney, NSW E-mail: john.pye@anu.edu.au The Compact Linear Fresnel Reflector (CLFR) is a concept for a large-scale line-focus solar concentrator for use in thermal power stations. A linear analogue of the 'central receiver' concept, it incorporates novel single-axis-tracking mirrors together with a line-focus direct-steam-generation thermal receiver. A transient model of direct steam generation in the CLFR thermal receiver is presented. This two-phase flow model uses Friedel pressure drops, and the simplifying assumptions of homogeneous flow and a stationary momentum equation. Dynamics are modelled using the numerical method of lines and a backwards difference formula DAE solver, and is performed using the free/open-source ASCEND modelling environment. During a step change in solar irradiation, a highly non-linear variation in exit flowrate is predicted and an explanation sought. We also present an investigation into the Ledinegg pressure/flowrate instability in the CLFR prototype. This instability arises from inflexion in the pressure-drop-versus-flowrate relationship during flow-boiling, but is seen to be stabilised by the addition of orifice plates upstream of the thermal receiver. A methodology for sizing these orifice plates is provided. A revised system model is presented incorporating the results of the above analysis. It is found that when the CLFR is run at a high exit steam quality, it gives only a slightly greater system efficiency, while increasing the risk of entry into the undesired superheat region. 1. BACKGROUND The Compact Linear Fresnel Reflector (CLFR) is a solar concentrator designed for use in large-scale thermal power stations. It produces steam by 'direct steam generation', which is to say that steam is generated directly in pipes rather than through the use of solarheated oil and a heat exchanger. Optically, the CLFR is arranged as a series of long mirrors arrayed underneath linear absorbers. The mirrors are individually motorised to track the sun daily from east to west. Above each group of twelve mirrors is located an elevated linear absorber containing a bank of high-pressure water pipes onto which the solar radiation is focussed. The absorber pipes are contained within an inverted trapezoidal cavity with a glass cover and rockwool-insulated steel top and sides; this cavity acts to reduce radiative losses and largely eliminates convective losses. The CLFR concept was first presented at the 1997 International Solar Energy Society meeting by Mills and Morrison [6]. Key aspects of the current design are direct steam generation as above, and that the linear Fresnel reflector is 'interleaved', meaning that the mirrors can be focussed at one of several absorbers, allowing denser packing of the mirror field. Mirrors are elastically deformed and adhered to a corrugated steel backing, reducing costs by comparison with sagged glass parabolic troughs. Mirror tracking is also performed via an innovative circular ring with chain drive.
Intensive development of the CLFR has taken place in recent years by Australian company Solar Heat and Power Pty Ltd, now continuing with a new US-based company called Ausra Inc., and has resulted an initial prototype 1,400 m² system completed at the Liddell power station in 2004 [5], with a second prototype 27,000 m² system approaching completion. The Liddell power station project has the end goal of using saturated steam from a third-stage 135,000 m² collector to provide a 36 MW solar augmentation to the coal power plant in the form of displaced high-pressure bleed steam in the final boiler feedwater heater; this will work towards Liddell power station meeting its obligations under the Mandatory Renewable Energy Target or possible future schemes. Major direct steam generation systems other than the CLFR include the DISS/INDITEP project approaching commercialisation stage in Spain [7] and the SolarMundo project understood currently to be seeking commercial-scale contracts [2]. 2. INTRODUCTION Direct steam generation involves a number of challenges. Firstly, the presence of twophase flow leads to difficulty in predicting the pressure drops and rates of heat transfer, compared to single-flow flow 1, which leads to greater uncertainty when design control algorithms, selecting pipe sizes, and sizing pumps and valves. Secondly, a pressure instability (called Ledinegg instability) occurs in two-phase flow that means that increasing the pumping flow rate can give a decrease in the pressure drop present in the pipe; this instability at best requires a more complex control system, and at worst could lead to damaging pressure and flow-rate oscillations. Thirdly, a direct steam generation system needs to be able to accommodate the ejection of most of the fluid present in the collector as it heats up from cold (full of water) to hot (mostly full of steam): for a closed-loop system this requires a 'surge tank' or similar, but is not a problem for open-loop systems. Finally, varying solar irradiation levels can cause problems in direct steam generation systems. If superheated steam is being generated, then there are (spatial) thermal gradients along the pipe; when irradiation varies, these thermal gradients move along the pipe causing local pipe temperature to vary quite rapidly. This can lead to high stresses and metal fatigue. Thermal and hydrodynamic analysis of CLFR as well as direct steam generation more generally has been the topic of ongoing research at the University of New South Wales under the supervision of Morrison. Odeh created a two-phase flow model of direct steam generation in a SEGS parabolic trough collector include a loss model for the evacuated tube metal-in-glass collector [16]. Reynolds and Jance performed some experimental modelling of heat loss from a trapezoidal cavity [18] and Reynolds also produced a hydrodynamic model based on the Martinelli-Nelson pressure drop correlation [4]. Other modelling of the direct steam generation process has recently been performed by Hirsch et al [21][20], with some system-level modelling of the DISS direct steam generation system based on parabolic trough collectors at the Plataforma Solar de Almería. An important difference between the present work and other modelling of direct steam generation is that this modelling has dealt with very long uninterrupted pipes of over 300 m length. This work also uses the more accurate Friedel pressure drop correlation, which 1 These difficulties arise from both uncertainties in empirical correlations for two-phase flow behaviour as well as the challenges of solving the advection problem for the two-phase flow case, which have been well documented in efforts made in the field of nuclear power plant engineering. Is Solar our only Nuclear option? ANZSES Solar 07 2
was previously shown to give improved agreement with experimental results for DISS systems [12]. An industry-standard steam propertes correlation [9] is also used, rather than interpolated data and bespoke curve-fits used by other workers. The model is implemented for use in a general purpose mathematical modelling environment called ASCEND [3]; this allows the absorber flow model to be connected with models for other components to create full system models, in a way that wasn't possible with the earlier UNSW work. 3. TRANSIENT FLOW MODEL A homogeneous one-dimensional two phase flow model can be derived from simple mass, energy and momentum balance, and treating the thermal mass of the absorber separately from the fluid. The resulting equations are t = 1 ṁ A z u = 1 t A 1 [ q ṁ h t z ] T w t = 1 w A w c p,w q s q l q t 1 ṁ A t = p z f 1 2 v 2 D v2 z where symbols have their usual meaning as defined by Incropera and DeWitt [17]. Here, v is the fluid velocity, subscripts 'w' correspond to the pipe wall, and subscripts for the heat flux q are as shown in Figure 1, including the solar flux at the absorber, the absorber heat loss and the heat transferred to the fluid. Figure 1: Inifinitesimal element in the one-dimensional homogeneous twophase flow model. The momentum equation is seen to introduce significant instability to the numerical model, as has been noted by Steward and Wendroff [8] and also by Hirsh et al [21], so the final equation is replaced by p z = f 1 2 v2 In additional to the above set of four differential-algebraic equations, fluid thermal- and physical-properties relationships are required to relate the variables {p, h, u, ρ, k, μ, T, x}. The last four of these are added because they are required in friction and heat transfer calculations. Fluid properties relations reresent some significant added complexity in the D Is Solar our only Nuclear option? ANZSES Solar 07 3
model, particularly as they must be designed to handle the two-phase flow case as well as any possible phase transitions and the discontinuities that result. For the calculation of f, the Friedel pressure drop correlation [15] is used in the two-phase region, and the Colebrook equation for single phase regions. The Friedel pressure drop correlation was used following the development of a steady-state absorber model that using this correlation that showed good agreement with experimental results from the DISS system in Spain [13][12]. Finally, heat transfer correlations are required. For the internal flow in the pipes, the Kandlikhar correlation is used [14]. For the cavity heat loss, a Nusselt-Grashof correlation is coupled with an approximate two-surface radiative transfer model developed in earlier work by et al [11]. The overall model is implemented as an equation-based model using the numercial Method of Lines in the mathematical modelling package ASCEND [3]. It is integrated using the (implicit) backwards difference formula algorithm as implemented in the opensource package IDA [1]. 3.1.Dynamic results A simulation of the CLFR absorber is presented here for a smaller-than-actual collector of length 100 m with inlet conditions of 150 C and 42 bar. There are 40 finite-difference nodes. The initial solar flux is set to 335 W/m for initial steady-state solution, and the step response is then calculated for a solar flux of 6000 W/m. This heat flux is sufficient to cause a transition from sub-cooled through saturated to superheated outlet. Steady-state is seen to be re-established at approximately 1100 s after the step-change. Transient response in fluid and pipe-wall temperature as well as exit enthalpy, steam quality and mass flow-rate are given in Figure 2. Is Solar our only Nuclear option? ANZSES Solar 07 4
Figure 2: Transient response, at absorber outlet, to a step increase in solar irradiation. It can be seen from the transient response that the mass flow rate peaks at over 0.5 kg/s before returning to a steady-state level of 0.26 kg/s. It is also of interest that the mass flow rate appears to begin increasing almost immediately, whereas it takes quite a long time for steady-state flow to return. Variation in mass flow rate also changes sharply at t = 250 s, when the exit flow first enters the saturation region (quality x>0). Finally, we see that the pipe wall temperature remains about 30 C above the fluid temperature, and its response lags that of the fluid temperature in the case of entry into the saturation region, but leads the response in the case of the initial step change, as expected. Of most concern in these results is the variation in the mass flow rate. It is seen that as the flow at the exit crosses the saturated liquid boundary, the mass flow rate increases sharply. This is as a result of the fluid in the pipe changing to gas, causing fluid in the pipe to be displaced at the outlet at a rate faster than the flow at the inlet. No such effect is seen when the outlet flow crosses the saturated gas boundary, as this latter boundary does not result in the same volumetric expansion as the former. The flow rate also changes quickly at the start, although this can be attributed to a thermal expansion of the fluid in single-phase state. The transient response given here should be expanded to cover a range of other transients including responses to negative steps in solar irradiation, and changes in inlet flow rate and pressure. Some numerical problems are still present in the model, but solutions have been proposed for these problems, including increasing the accuracy of the derivative calculations used for the system Jacobian [10]. These areas are proposed for further investigation. 4. LEDINEGG PRESSURE INSTABILITY Instability occurs in flow-boiling in general, as a result of the changing wall shear stress for subcooled, saturated and superheated flow. This instability, called Ledinegg instability, can be explained by considering the case where steady flow boiling occurs in a pipe at high flow rate such that the pipe outlet sees saturated steam at quality of 50%. It can be seen from the energy balance that decreasing the flow rate will cause the outlet quality of the steam to rise, and it follows that the length of pipe occupied by fluid in a two-phase state will grow. The result of these effects is that there is a smaller portion of the pipe containing high-viscosity, high-friction liquid flow, and a larger portion of the pipe containing fluid of lower viscosity and causing lower pipe friction. For conditions of practical interest, this results in a reduction in overall pressure drop as flow rate increases. The standard solution for Ledinegg instability is to introduce pipe orifices upstream of the flow boiling region [14]. This adds a significant additional pressure drop in the part of the pipe containing the subcooled flow, which is proportional to the square of flow velocity. The effect of this additional pressure drop is to 'tilt' the overall pressure-versus-flowrate curve such that it no longer contains a negative gradient for any interval of flow rates. Using a steady-state model of the full-scale CLFR Stage 2 design, it was found for an inlet pressure of 44 bar and inlet temperature of 175 C, an orifice ratio of less that 0.4 would be required to ensure the pressure-versus-flowrate relationship was monotonically increasing, a necessity in order to make the system controllable using pressure signals. This orifice ratio is defined as the ratio of the orifice diameter to the pipe inside diameter. If lower pressures and inlet temperatures are allowed for, the required orifice ratio becomes approximately 0.325. Figure 3 shows the results for the 44 bar, 175 C inlet conditions. The above modelling relates to a simple analysis of just the absorber and upstream orifice. All twelve pipes in the absorber area treated as having identical flow rate and pressure drop, which is in fact unlike to be be realistic. Firstly, if this instability is present Is Solar our only Nuclear option? ANZSES Solar 07 5
in an individual tube then it will be necessary for orifices to be attached upstream of each individual pipe. Natan, Barnea and Taitel investigated two phase flow in parallelconnected pipes and predicted this instability using a similar model [19]. Secondly, even if the stability in the absorber is neutralised, it is still possible that instability could arise between absorbers, due to differences the length of pipe conneting an absorber to the steam drum, as seen in Figure 4. It is therefore proposed that orifices upstream of the absorber would need to be of different diameters to attempt to equalise the flow through each absorber. Modelling of absorbers with different downstream pipework lengths but equal overall pressure drop showed that without modified upstream orifice, approximately 7% more flow would go down the short flow path, with the result that the quality at the exit of the short connecting pipe would be 0.72 if the flow rate were set to give an exit quality of 0.8 at the exit of the long connecting pipes. Figure 3: Ledinegg instability for pressure drop in a Stage 2 CLFR absorber combined with upstream orifice, with upstream pressure 44 bar and temperature 175 C. As the orifice ratio D orif /D pipe is varied, the instability is removed and the pressure drop versus flow rate relationship becomes monotonic. 5. REVISED SYSTEM MODEL Over the course of the CLFR design and prototype process, the concept for integration of the collector with the power station has changed significantly. Initially cautious plant engineers required the use of a heat exchanger to isolate the CLFR flow loop from the main power station coolant loop. In more recent designs, this heat exchanger has been eliminated. The result has been that the closed-loop fixed-volume, fixed-mass pressure problems that occurred with that system have been eliminated. The 'surge tank' present in earlier designs has thus been removed, and replaced by a smaller steam drum, located up in the air slightly above absorber height, for the purpose of ensuring that the absorber can be fully charged with water at the time of startup. A new system model was therefore developed using pipe pressure drop models, minor losses, quadratic pump curves, control valve, CLFR absorber and thermal loss model, and orifice plates sized to eliminate the Ledinegg instability as above. The model was built up using equation-based models using the ASCEND modelling Is Solar our only Nuclear option? ANZSES Solar 07 6
environment. This has the advantage of allowing different system parameters to be 'fixed' and 'freed'; ASCEND precedence-orders the variables in the system and solves for the unknowns in the necessary sequence. It is important to note that a system model of a direct steam generation system requires some significant detail in the model of the absorber. Without a model that includes mass hold-up and and two-phase flow, the correct heat transfer and pressure drop results can not be obtained, and these phenomena are central to being able to predict the system operating point. The only major simplification being made here is the removal of the transient momentum equation, on the basis that the speed-of-sound pressure waves predicted by that equation are too fast to be of interest here, as opposed to in models of nuclear reactor 'loss of coolant' events where they can be of critical importance in the first few milliseconds after a leak develops. 5.1.Results A number of scenarios and design investigations were performed using the system model. Standard operating conditions were selected to be 7.7 kg/s per CLFR module, with an outlet pressure of 42 bar. This requires a pressure drop through the pump-plus-controlvalue of 1.1 bar. The control value present immediately downstream of the pump has been given a design pressure drop of 0.55 bar for system controllability, resulting in a required pump pressure of 1.6 bar. At the design point, the collector efficiency was estimated to be 92%. The pump efficiency for the design point, for the over-sized pump selected for installation on the prototype, was estimated to be 56%. The net absorbed heat per module of three absorbers is 13 MW, with the absorbers being 310 m long and containing 12 pipes each, and with an effective concentration ratio (after optical losses) of 27. Pumping power is 2.1 kw. Figure 4: The modelled CLFR system module with three absorbers, a steam drum and a pump, plus associated pipework. 6. CONCLUSIONS A transient two-phase flow model was created and was shown to exhibit qualitatively plausible results. Experimental results from the Stage 2 prototype will be used to verify this model once they are available. The elements of the transient model were incorporated into an improved overall system Is Solar our only Nuclear option? ANZSES Solar 07 7
model including thermal absorber, cavity heat loss, connecting pipework, pumps, control values, steam drum, and orifice plates. This model was used to size the orifices to avoid the Ledinegg instability, and then to size the control valve and reticulation pump. Further work on the model is proposed, including overcoming some software limitations with the transient model and validation of the computed results once experimental data becomes available. 7. REFERENCES [1] A. C. Hindmarsh, 2000, The PVODE and IDA Algorithms, LLNL. [2] Art Westerberg and Benjamin Allan and Vicente Rico Ramirez and Mark Thomas and Kenneth Tyner, 1998, ASCEND IV: Advanced System for Computations in ENgineering Design, Department of Chemical Engineering, Carnegie Mellon University. [3] D J Reynolds and M Behnia and G L Morrison, 2002, A Hydrodynamic Model for a Line Focus Direct Steam Generation Solar Collector, Proceedings of ANZSES Solar 2002, Newcastle, Australia. [4] D R Mills and le Lievre, P and G L Morrison, 2004, First Results from Compact Linear Fresnel Reflector Installation, Proceedings of ANZSES Solar2004. [5] David R Mills and Christopher J Dey, 1999, Transition strategies for solar thermal power generation, Proceedings of the International Solar Energy Society Conference 1999. [6] H. Bruce Stewart and Burton Wendroff, 1984, Two phase flow: Models and methods, Journal of Computational Physics, vol 56 pp 363 409. [7] IAPWS, 1997, Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, The International Association for the Properties of Water and Steam. [8] John D and Graham L Morrison and Masud Behnia, 2003, Modelling of Cavity Receiver Heat Transfer for the Compact Linear Fresnel Reflector, Solar World Congress 2003. [9] John D and Graham L Morrison and Masud Behnia, 2006, Pressure drops for direct steam generation in line focus solar thermal systems, Proceedings of the Australian and New Zealand Solar Energy Society. [10] Jurgen Rheinlander and Markus Eck, 2002, Direct Solar Steam (DISS) Research Project on Direct Solar Steam Generation (DSG) in Parabolic Trough CollectorsTask 400 DSG Applied Research Document DISS SC MI 03 Numerical Modelling of Pressure Losses, ZSW. [11] Lienhard, John H (V) and Lienhard, John H (IV), 2006, A Heat Transfer Textbook, Phlogiston Press [12] Masud Behnia, 2002 Selected Topics on Two Phase Heat Transfer, unpublished. [13] Odeh, S D, 1999, Direct Steam Generation Collectors for Solar Electric Generation Systems (Thesis), University of New South Wales. [14] P F Incropera and D P DeWitt, 1996, Fundamentals of Heat and Mass Transfer, Wiley, USA Is Solar our only Nuclear option? ANZSES Solar 07 8
[15] Reynolds, D J and Jance, M J and Behnia, M and Morrison, G L, 2004, An experimental and computational study of the heat loss characteristics of a trapezoidal cavity absorber, Solar Energy, vol 76 pp 229 234. [16] Tobias Hirsch and Markus Eck, 2006, Simulation of the Start Up Procedure of a Parabolic Trough Collector Field with Direct Solar Steam Generation, Modelica 2006. [17] Tobias Hirsch and Markus Eck and Wolf Dieter Steinmann, 2005, Simulation of transient two phase flow in parabolic trough collectors using Modelica, Modelica 2005. Is Solar our only Nuclear option? ANZSES Solar 07 9