COMPUTATIONS OF THE FLUID FLOW IN STRATIFICATION PIPES FOR SOLAR STORAGE TANKS

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1 COMPUTATIONS OF THE FLUID FLOW IN STRATIFICATION PIPES FOR SOLAR STORAGE TANKS ABSTRACT S. Göppert, R. Lohse, T. Urbaneck, U. Schirmer, B. Platzer, P. Steinert Chemnitz University of Technology Department of Technical Thermodynamics Reichenhainer Str Chemnitz, Germany Tel: The efficiency of solar systems is strongly influenced by the quality of the thermal stratification in the storage tank. Fluid mechanical charge systems are often used to generate and maintain a thermal stratification. Such systems cause, however, undesirable sucking effects. Therefore, the knowledge of the appearing fluid flows as well as the knowledge of the consequences of constructive changes are very important for the design of such charge systems. However, simulations with CFD (Computational Fluid Dynamics) and experimental investigations are very costly and time-consuming. In this article a new and much simpler computation method is introduced making the determination of the individual fluid flows and the estimation of the effects of constructive changes possible. The computations can be carried out within short time. The comparison with CFD gives a qualitatively good agreement. The results of a constructive modification of a simple charge system reducing the suction are discussed. 1. INTRODUCTION A thermal stratification of the fluid makes sense for the storage of thermal energy. Zurigat and Ghajar (2002) show that in comparison to mixed storage tanks an improvement of the efficiency of solar systems of 5-20 % is possible by the generation of a thermal stratification. This stratification must be generated and received by suitable charge systems. Often fluid mechanical charge systems based on the gravitation principle are used for it (Göppert et al., 2008). Simple pipes with circular openings are widespread. Besides, there is also a lot of especially developed stratifiers. These constructions have differently formed, but always vertically arranged outlets. The fluid has to stratify in the right height of the tank according to its density. However, it is known that different sucking effects can appear due to pressure differences between the charge system and the storage tank during the charge process (Shah et al., 2005; Lohse et al., 2008). Thereby, fluid from the storage tank is sucked into the charge system. This leads to a mixing with the charge flow and subsequently to a worse stratification behaviour. According to the arrangement of the charge system in the tank and to the flow circumstances, either warm water from the upper storage area (see Fig. 1 a)) or colder water from the lower storage area (see Fig. 1 b)) is sucked. The following open questions arise from this mixing behaviour: How much fluid is sucked from the storage tank? Are there better and worse charge systems concerning the suction? Is it possible to estimate the effect of constructive changes?

2 Computations with CFD and experimental investigations are costly and time-consuming. In practice this is often not acceptable, e.g. for the adaptation of available charge constructions to different storage tank dimensions and geometries. A tool would be helpful for the development and dimensioning of charge systems making suitable computations possible in a relatively simple and quick way. In the following a new computation method offering this possibility is introduced. The algorithm was implemented in MatLab. The time needed for an arithmetic calculation lies within few minutes. Fig. 1: Sucking effects in fluid mechanical charge systems (1 sucked fluid flow, 2 charge flow): a) suction of warmer water, b) suction of colder water 2. COMPUTATION METHOD The Bernoulli equation complemented by the pressure losses forms the basis of the new computational method. To convey a fluid flow by a charge system, the flow resistance must be overcome by a pressure difference. Thus, the charge requires a certain inlet pressure in the charge system. The aim is the computation of the resulting pressure distribution in the charge system as well as the in- or outflowing mass. The vertical pressure distribution in the tank arises from the hydrostatic pressure where the temperature-dependent density has to be taken into consideration. It is valid as condition for the pressure that the static pressure in the discharge openings is equal to the static pressure in the tank in case of outflow into the tank. Thus, the respective mass flows can be calculated from the pressure differences over the branch pipes. The solution of the problem is not explicitly available and has to be determined iteratively. The density, the specific heat capacity, and the viscosity of the fluid (here: water) are needed for the computation. All properties are determined according to IAPWS (1997). On the one hand, the pressure losses are computed for the straight pipe segments and on the other hand for different pipe installations and single flow resistances. For a flow in a straight pipe the pressure loss can be determined with the help of the pipe friction factor. With it, a resistance coefficient can be formed. The pipe friction factor depends on the Reynolds number and on the roughness of the pipe. It can be easily computed with one of the well known equations for pipe flow. For laminar flow the pipe friction factor depends only on the Reynolds number. For turbulent flow the influence of the roughness, which must be known for the computation of the pipe friction factor, plays an important role. Three cases are distinguished: hydraulically smooth (Sigloch, 2005; explicit form of the equation according to Prandtl), hydraulic transitional range (Zigrang and Sylvester, 1982; explicit form of the equation according to Colebrook), hydraulically rough (Nikuradse, in 1933).

3 Pressure losses in pipe installations or single resistances can be also summarised in a resistance coefficient. Generally, these resistance coefficients are dependent on the Reynolds number, the geometrical dimensions, and the roughness. Turbulent flow and hydraulically rough behaviour dominate often in the technical applications. Then the resistance coefficient like the pipe friction factor is independent of the Reynolds number. However, relatively moderate to low Reynolds numbers appear in the charge systems examined here to prevent the generation of strong flows in the tank. Laminar flow can occur in certain areas. Here, information of the dependence of the respective resistance coefficients on the Reynolds number are necessary. Nevertheless, only constant approximated values are often found in the literature. Idelchik and Steinberg (1996) deliver the most comprehensive and most detailed representation of resistance coefficients. A likewise good, however, more compact representation gives Wagner (1992). The equations and coefficients of both publications are used for the computations. A flow merging or a flow separation can occur at the flow junctions. A negative pressure difference between the main pipe and the storage tank over a branch leads to sucking of fluid from the tank and a mixing with the charge flow. A positive pressure difference leads to a partial or complete outflow over the respective branch. Both processes are shown in Fig. 2. Two resistance coefficients are determined for each case, for the branch and for the straight passage, using the equations given in Wagner (1992). In addition, the continuity equation for both cases and the law of conservation of energy (with neglect of the kinetic energy) for a flow merging in the view of mixing must be taken into consideration. Fig. 2: Flow relations in a t-piece of a fluid mechanical charge system a) flow merging, b) flow separation The structure of the developed program is shown in Fig. 3. At the beginning of the computation the geometry data of the storage tank and the charge system, the temperature distribution in the tank, the charge temperature, as well as the value for the truncation criterion must be given. Then, the discharge opening that is next to the layer with the same temperature as the charge fluid is determined. Starting from this discharge opening, an initial value for the entrance pressure is estimated. In reverse direction pressures, temperatures, and mass flows along the charge system are computed now. The condition p p, p, p 0 is used for the last discharge opening, from which mp i st i loss fluid flows into the tank. Since the initial value for the entrance pressure is determined without consideration of pressure losses, it is too low. Therefore, a negative p results. Now, the entrance pressure is increased gradually until a positive value is reached. Thus, two limit values are available for the entrance pressure. Using an iterative computation, p becomes smaller until the truncation criterion is fulfilled. At last, a tabulation of the computed data and diagrams are provided.

4 Fig. 3: Flow chart of the developed program The simplifications introduced here limit the application of the model: The flow in the charge system must occupy the whole pipe cross section. Constant velocity and fluid properties over the flow cross section are assumed. The Bernoulli equation and the resistance coefficients are valid for constant density. However, the dependence of the density on the temperature forms the basis of fluid mechanical charge systems by impacting on the pressure difference between storage tank and pipe. But this dependence is only very low (deviations to mean density < 2 %). Therefore, the computation is a very good approximation. The resistance coefficients have been determined empirically for selected cases. Between the literature references considerable differences exist. No or only vague information about resistance coefficients are available for certain constructions. The possible interactions of the resistances are neglected in the model. With the introduced computation only instantaneous constellations are considerable. 3. COMPUTATIONS Computations were carried out exemplarily for two different charge designs and for the same conditions to verify the operation of the program: a simple charge system with short horizontal branches (system A) as well as the ConSens charge system (system B). System B contains a constructive modification of system A by which the junctions get a height difference to the discharge openings. The sucking of fluid from the storage tank should thereby be reduced or avoided. Both charge systems are shown in Fig. 4.

5 The charge behaviour was calculated for V 10 m 3 /h and two different stratifications. Both given stratifications are shown in Fig. 5. The course follows a hyperbolic tangent. The position of the middle temperature lies at a height of 1.3 m and, therefore, approximately halfway between the second and third outlet. The zero of the height variable is located at the water level. The charge temperature is the middle temperature of the respective stratification. Fig. 4: Examined charge designs Fig. 5: Two given stratifications in the a) simple charge system (system A), storage tank b) ConSens charge system (system B) Two comparative computations with CFD were carried out for system A to validate the new algorithm. The results of both computations are shown in Fig. 6. The sucked fluid flows are a little larger in the computations with MatLab than the fluid flows in the CFD simulations, however, they agree relatively well. There are stronger divergences for the distribution of the fluid flow on the second and third outlet. Here, clearly higher mass flows are calculated with the simple MatLab program in the upper outlet. CFD simulations have shown that in contrast to the model assumption no complete mixing exists between the sucked fluid and the charge flow. The fluid remaining in the main pipe below the second outlet is, therefore, colder than the one with entire mixing. This could be the reason for the fact that the outflow is stronger at the higher outlet for the computations with MatLab. Larger density differences allow to expect a forced suction. This is confirmed by the simulation results for the second stratification case in Fig. 6. The temperature rises as a result of the mixing in the charge system and the outflow shifts upwards from the third to the second outlet. These trends are also properly reproduced by the MatLab algorithm. In the CFD simulation suction occurs in the fourth outlet, too, for the second stratification case. This is due to the fact that the outflow from the third outlet does not fill the whole cross section anymore as a result of the larger density differences. A free shear layer develops by which the nearby quiescent fluid from the charge system is carried away. Fluid is sucked from the storage tank through outlets located further downwards. This process cannot be described with the new computation method due to the assumptions used.

6 Fig. 6: Computed mass flow rates for MatLab and CFD with a) stratification 1 and b) stratification 2 Fig. 7: Vertical distribution of the pressure difference between the main pipe and the store with a) stratification 1 and b) stratification 2 The pressure difference between the main pipe of the charge system and the storage tank arises from the computation of the static pressure at both points. In Fig. 7 the vertical distributions of this pressure difference are compared for the examined charge designs. The diagrams show that the pressure differences are only very small, a few Pascal only. Besides, it has to be noted that the outlet openings lie higher than the junctions for system B. Together with greater density differences this height difference can lead to a lower pressure in the junctions than in the storage tank (see third junction in Fig. 7 b)) whereas the pressure difference over the whole branch is still positive (pressure difference at the outlet position). The already described entrainment of the fluid from the lower area is still strengthened for the case that the cross section is not completely filled by the charge flow. The computed mass flow rates are shown in Fig. 8. A positive mass flow stands for suction. A negative mass flow indicates that the fluid flows out of the charge system. The fourth junction as well as the bottom of the charge system is marked by small lines. According to Fig. 7, the pressure in the storage tank is higher than in the charge system at the first junction for both variations. Suction occurs here. However, the pressure difference is

7 clearly smaller for system B, so that in comparison to system A reduced suction occurs (approximately % less). This also shows the representation of the mass flow rates in Fig. 8. Consequently, the application of inclined branches leads to a clear reduction of the suction and a lower reduction of stratification. Fig. 8: Computed mass flow rates for system A and system B with a) stratification 1 and b) stratification 2 Positive pressure differences appear at the second and the third junctions. Here, the fluid from the charge system enters the storage tank. The pressure difference over the branch is important for the second charge design because of the height difference. This pressure difference must be positive for an inflow in the storage tank. This is the case for both stratifications. For system A and the first stratification 74.1 % of the primary inflow pass the second and 51.7 % the third outlet. For the second stratification these are % and 31.3 %. The layer which corresponds to the charge temperature of 75 C lies approximately in the middle between both outlets. However, the temperature of the fluid rises in the charge system by the suction, so that clearly more fluid flows out of the second outlet than of the third one. This shift becomes larger with increasing suction (cf. Fig. 8). For system B and the first stratification the mass flows amount to 58.2 % in the second and 53.8 % in the third outlet. Here, an almost uniformly distributed inflow through both outlets occurs. For a smaller suction the temperature in the charge system also rises less compared to the first variant. Another advantage lies in the fact that the whole outflow is only 12 % larger than the primary inflow and, thereby, the discharge velocity decreases in comparison. The mixing in the storage tank is reduced by the lower velocities. For system A the whole outflow is 25.8 % larger than the primary inflow. The flow at the second outlet of the charge system is stronger for a higher suction (see Fig. 8): the 1.8-fold of the fluid flow in the third outlet for system B and the 3.7-fold for system A. Thus, the reduced suction of system B improves the charge behaviour and with it the build-up and the preservation of a stratification. Experimental investigations of Lohse et al. (2008) confirm this, too. 4. CONCLUSIONS The fluid flows appearing in two different fluid mechanical charge systems could be calculated successfully with the introduced computation method. The existing divergences to CFD simulations result from the fact that the flows calculated with CFD have more realistic

8 assumptions. However, the charge behaviour is properly described. The trends for changes of the conditions (e.g. stratification, design) agree with the numerical simulation results and experimental investigations. Thus, constructive changes lead to reduced suction and to improved charge behaviour. The effects of constructive changes can be estimated well with the introduced simple computation method. Now, the algorithm should be extended for the investigation of other outlet geometries. The development of the algorithm up to the computation of complete charge processes is conceivable in principle, but the realisation is much more complex. ACKNOWLEDGEMENT This work was financially supported with resources of the Federal Ministry of environment, nature conservation and reactor security under the sign of promotion A. The authors are grateful for the support of the Project Management Organization Jülich. The responsibility for the content of this release is borne by the authors. NOMENCLATURE C truncation criterion (Pa) Subscripts h height (m) b bottom m mass flow rate (kg/s) ch charging p pressure (Pa) i control variable r ratio (%) mp main pipe t temperature ( C) st storage tank u velocity (m/s) t top V volume flow rate (m 3 /s) 1,2,3 locations REFERENCES Göppert, S., Urbaneck, T., Schirmer, U., Lohse, R., Platzer, B. (2008). Be- und Entladesyteme für thermische Schichtenspeicher: Teil 1 Überblick. Chemie Ingenieur Technik 80, IAPWS (1997). Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. Available at Idelchik, I.E., Steinberg, M.O. (Ed.) (1996). Handbook of hydraulic resistance, third ed. Begell House, New York. Lohse, R., Göppert, S., Kunis, C., Urbaneck, T., Schirmer, U., Platzer, B. (2008). Be- und Entladesysteme für thermische Schichtenspeicher: Teil 2 Untersuchungen des Beladeverhaltens. Chemie Ingenieur Technik 80, Nikuradse, J. (1933). Strömungsgesetze in rauhen Rohren. VDI-Forschungsheft 361, Berlin., Beilage zu Forschung auf dem Gebiet des Ingenieurwesens, Ausgabe B, Band 4, Juli/August. Shah, L.J., Andersen, E., Furbo, S. (2005). Theoretical and experimental investigations of inlet stratifiers for solar storage tanks. Applied Thermal Engineering 25, Sigloch, H. (2005). Technische Fluidmechanik. Springer, Berlin. Wagner, W. (1992). Strömung und Druckverlust. 3. Aufl. Vogel (Kamprath-Reihe), Würzburg. Zigrang, D.J., Sylvester, N.D. (1982). Explicit approximations to the solution of Colebrook s friction factor equation. AIChE Journal 28, Nr. 3, Zurigat, Y.H., Ghajar, A.J. (2002). Heat transfer and stratification in sensible heat storage systems. In: Dinçer, I., Rosen, M.A. (Eds.), Thermal Energy Storage, Wiley, Chichester,