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New computation method for stratification pipes of solar storage tanks
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Solar Energy 83 (2009) 1578–1587 www.elsevier.com/locate/solener
New computation method for stratification pipes of solar storage tanks Stefan Go¨ppert *, Rolf Lohse, Thorsten Urbaneck, Ulrich Schirmer, Bernd Platzer, Philipp Steinert Department of Technical Thermodynamics, Chemnitz University of Technology, Reichenhainer Str. 70, 09126 Chemnitz, Germany Received 22 August 2008; received in revised form 11 May 2009; accepted 18 May 2009 Available online 11 June 2009 Communicated by: Associate Editor Halime Paksoy
Abstract The efficiency of low-flow solar systems is strongly influenced by the quality of the thermal stratification in the storage tank. The better a thermal stratification can be generated and maintained, the higher can be the yield of the solar system. Fluid mechanical charge systems are often used for this purpose, which 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) 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 for a simple charge system. The results of a constructive modification of the charge system reducing the sucking effect are discussed. The remaining quantitative differences result from the discrepancies between the non-ideal behaviour of the real fluid and the model assumptions and point out improvement potentials. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Solar storage tanks; Inlet stratifiers; Computation
1. Introduction A thermal stratification of the fluid makes sense for the storage of thermal energy in low-flow solar systems. Zurigat and Ghajar (2002) show in an overview 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 (Go¨ppert et al., 2008). Simple pipes with circular openings are widespread. Besides, there is also a lot of especially developed stratifiers, e.g. the respective patented charge systems of the ConSens *
Corresponding author. Tel.: +49 371 531 34749; fax: +49 371 531 800075. E-mail address: [email protected] (S. Go¨ppert). 0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.05.007
GmbH, Solvis KG and Sailer GmbH (Lohse et al., 2008; Andersen et al., 2008). 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. 1a) or colder water from the lower storage area (see Fig. 1b) is sucked. In the first case the usable temperature level decreases by cooling the upper area. In the second case the supply temperatures for the solar circuit rise by warming the lower area. The German
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Nomenclature a A c C d g h k l m m_ p r Re t u
area ratio () area (m2) specific heat capacity (kJ/kg/K) truncation criterion (Pa) diameter (m) acceleration due to gravity (m/s2) height (m) roughness (m) length (m) mass flow ratio () mass flow rate (kg/s) pressure (Pa) ratio (%) Reynolds number (–) temperature (°C) velocity (m/s)
V_ a q f k
volume flow rate (m3/s) departure angle (°) density (kg/m3) resistance coefficient (–) pipe friction factor (–)
Subscripts b bottom ch charging i number of respective junction mp main pipe st storage tank t top w water 1,2,3 locations
company Solvis is using check valves in their stratifiers to avoid such sucking effects. In this work only charge systems without check valves are considered. The following open questions arise from the explained mixing behaviour:
method and the underlying model offering this possibility are introduced. The algorithm resulting from the new model was implemented in MatLab. The time needed for an arithmetic calculation lies within few minutes.
How much fluid is sucked from the storage tank? Are there better and worse charge systems concerning the sucking? Is it possible to estimate the effect of constructive changes?
2. Computation method
Computations with CFD are costly and time-consuming. This is also true of experimental investigations. 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
2.1. Model The Bernoulli equation complemented by the pressure losses forms the basis of the new computational method: X q q f : ð1Þ p1 þ q1 gh1 þ 1 u21 ¼ p2 þ q2 gh2 þ 2 u22 1 þ 2 2 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. Vice versa a given inlet pressure causes a certain volume flow. In the developed algorithm the volume flow
Fig. 1. Sucking effects in fluid mechanical charge systems. (1) Sucked fluid flow, (2) charge flow. (a) Sucking of warmer water, (b) sucking of colder water.
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is given. 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 but has to be determined iteratively. 2.2. Pressure losses 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: l f¼k : d
ð2Þ
The pipe friction factor depends on the Reynolds number and on the roughness of the pipe. It can be computed with one of the following equations. For laminar flow the pipe friction factor depends only on the Reynolds number: k¼
f ¼ f ðRe; geometrical dimensions; kÞ:
ð7Þ
For longer segments, as for example curve or elbow, the losses of the pipe flow after Eq. (2) possibly have to be added to the resistance coefficients. Turbulent flow and hydraulically rough behaviour dominates 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. 2.3. Flow junction
64 : Re
ð3Þ
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): k¼
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:
0:309 ðlg Re 0:845Þ
2
for : Re
k < 65; d
ð4Þ
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).
hydraulic transitional range (Zigrang and Sylvester, 1982; explicit form of the equation according to Colebrook):
1 k 5:02 k 5:02 k 13 pffiffiffi ¼ 2 lg lg lg þ 3:7d Re 3:7d Re 3:7d Re k ð5Þ hydraulically rough (Nikuradse, 1933): k¼
1 ð2 lg dk þ 1:14Þ2
for : Re
k > 1300: d
ð6Þ
In the hydraulically rough range the pipe friction factor becomes independent of the Reynolds number.
Fig. 2. Flow relations in a t-piece of a fluid mechanical charge system. (a) Flow merging, (b) flow separation.
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The equations for flow merging are f2 ¼ 0:92ð1 mÞ2 þ mð1 mÞð2 aÞ cos a 1 1a m2 1:2 1 þ 0:8 1 2 cos a ; a a a ð8Þ 2
f3 ¼ 0:03ð1 mÞ þ mð1 mÞð2 aÞ h cos a i m2 1 þ 1:62 1 0:38ð1 aÞ ; a where m ¼ m_ 2 =m_ 3 and
a ¼ A2 =A3 :
The equations for flow separation are 1 a 2 cot f2 ¼ 0:95ð1 mÞ þ 0:4mð1 mÞ 1 þ a 2 a 0:4 0:1a ; þ m2 1:3 cot 0:3 þ 2 a2 2
ð9Þ ð10Þ ð11Þ
ð12Þ
f1 ¼ 0:03ð1 mÞ 0:2mð1 mÞ þ 0:35m2 ;
ð13Þ
where m ¼ m_ 2 =m_ 1
ð14Þ
and
a ¼ A2 =A1 :
ð15Þ
The continuity equation for both cases (with positive sign for flow merging and negative sign for flow separation) is: u3 q3 A3 ¼ u1 q1 A1 u2 q2 A2 :
ð16Þ
In addition, the law of conservation of energy must be taken into consideration for a flow merging in the view of mixing. Neglect of the kinetic energy yields: m_ 3 cw;3 t3 ¼ m_ 1 cw;1 t1 þ m_ 2 cw;2 t2 :
ð17Þ
In the case of outflow the boundary from vertical tube to tank (see position 2 in Fig. 2b) is used in the Bernoulli equation and the zetas of the junction and the branch are filled in. For flow merging, however, position 2 is in the tank because the velocity and therefore the static pressure at the opening are unknown. 2.4. Fluid properties The density, the specific heat capacity, and the viscosity of the fluid (here: water) are needed for the computation. All properties are determined in dependence on pressure and temperature being particularly important for the density. Therefore, the algorithms according to IAPWS (1997) are used. 2.5. Program sequence 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.
Fig. 3. Flow chart of the developed program.
Starting from this discharge opening, an initial value for the entrance pressure is estimated regarding only the hydrostatic pressure. In reverse direction pressures, temperatures, and mass flows along the charge system are computed now using the above equations. The condition Dp ¼ pmp;i pst;i Dploss ¼ 0
ð18Þ
is used for the last discharge opening, from which fluid flows into the tank. Since the initial value for the entrance pressure is determined without consideration of pressure losses, it is too
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low. Therefore, a negative Dp results. Now, the entrance pressure is increased gradually until a positive value is reached. Thus, two limit values are available for the entrance pressure. The iterative computation begins with the lower value. Then, the difference between the two limit values is halved in each step. The respective pressure is used as new lower or upper limit depending on whether Dp < 0 or Dp > 0. Using this iterative computation, Dp becomes smaller until the truncation criterion (here: C = 106 Pa) is fulfilled. At last, a tabulation of the computed data and diagrams are provided. 2.6. Restrictions 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 for the computations. 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 for pipe flow junctions or single resistances 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 and the resistance coefficients are taken into consideration individually. With the introduced computation only instantaneous constellations are considerable, however, no temporal charge.
Both charge systems are shown in Fig. 4. The main dimensions are the same for both variants. For charge system B the branches and the main pipe include an angle of 45° oppositely to the flow direction. The junctions, thereby, lie below the outlets. The outlets themselves lie on the same height for both variants. The charge behaviour was calculated for a volume flow rate of 10 m3/h and two different stratifications. Both given stratifications are shown in Fig. 5. The course follows a hyperbolic tangent. The temperature of the upper layer amounts to 80 °C and the temperature of the lower layer to 70 °C and 50 °C, respectively. 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 cover of the storage tank or alternatively at the water level for pressureless stores. The charge temperature is the middle temperature of the respective stratification.
3. Computations 3.1. Examined charge designs 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 (charge system A) as well as the ConSens charge system (charge system B). The charge system B contains a constructive modification of the charge 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.
Fig. 4. Examined charge designs.
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Fig. 5. Two given stratifications in the storage tank.
3.2. Comparison with CFD The fluid flow is investigated by means of three-dimensional CFD calculations using the commercial software package ANSYS CFX 11 (Ansys Inc., 2007). A SST k-x model extended for free convection is used to simulate the turbulent transport processes in the store. The properties for water are specified temperature-dependent. The cylindrical tank is set to 4 m in height as well as diameter providing a volume of approximately 50 m3. With a flow rate of 10 m3/h the store represents a short-term store. Fig. 6 shows a section of the grid. The whole grid comprises 530,000 elements. The computational model was validated against experimental data of a 0.6 m3 thermal energy store in earlier work (Lohse et al., 2008). The computed velocity field and temperature distribution for this experimental store are shown in Figs. 7a and 8a at the beginning of
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charge. In a further article a comparison of the new algorithm to experimental investigations with schlieren photography will follow. But this is beyond the scope of this article. Two comparative computations with CFD were carried out for the charge system A to validate the new algorithm. In Fig. 7b and c the respective velocity fields and in Fig. 8b and c the respective temperature distributions in the charge system and the tank are to be seen. The same behaviour occurs in the fluid flow as for the 0.6 m3 store. It only depends on the given stratification. This confirms the accuracy of the simulations for small and medium sized tanks. The numerical results of both computations are shown in Table 1. A positive mass flow stands for suction. A negative mass flow indicates that the fluid flows out of the charge system. 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 (Lohse et al., 2006, 2008). 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 Table 1. 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. Corresponding figures are shown in Lohse et al. (2008). 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. 3.3. Comparison of both charge systems
Fig. 6. Grid spacing in and nearby the charge system A.
These computations are carried out with the new method. 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. 9 the vertical distributions of this pressure difference are compared for the examined charge designs. The pressure differences over the branches cause the mass flows
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Fig. 7. Velocity field in the charge system A and the storage tank computed with CFD. (a) 0.6 m3 store, tch = 41.4 °C, V_ = 0.14 m3/h, tst,t = 58.7 °C, tst,b = 22.3 °C, h(tst = 41.4 °C) = 0.4 m; (b) 50 m3 store, tch = 75 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m; (c) 50 m3 store, tch = 65 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m.
out of or in the charge system. 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 the charge 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. 9b) 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 com-
pletely filled by the charge flow. The computed mass flow rates are shown in Fig. 10 or Fig. 11, respectively. The fourth junction as well as the bottom of the charge system is marked by small lines. Table 2 summarises the computed values of the in- and outflows, of the mean velocities in the outlets, and of the percentage ratios based on the primary inflow. According to Fig. 9, 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 clearly smaller for the charge system B,
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Fig. 8. Temperature distribution in the charge system A and the storage tank computed with CFD. (a) 0.6 m3 store, tch = 41.4 °C, V_ = 0.14 m3/h, tst,t = 58.7 °C, tst,b = 22.3 °C, h(tst = 41.4 °C) = 0.4 m; (b) 50 m3 store, tch = 75 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m; (c) 50 m3 store, tch = 65 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m. Table 1 Comparison of fluid flows computed with MatLab and CFD for the charge system A (see Fig. 4a). Method
MatLab
CFD
tch = 75 °C, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m, V_ = 10 m3/h Parameter m_ (kg/s) r (%) Charge 2.708 100.0 1. Outlet 0.699 25.8 2. Outlet 2.007 74.1 3. Outlet 1.400 51.7 4. Outlet 0 0
u (m/s) 0.088 0.041 0.117 0.081 0
m_ (kg/s) 2.690 0.602 1.520 1.772 0
r (%) 100.0 22.4 56.5 65.9 0
u (m/s) 0.088 0.035 0.088 0.103 0
tch = 65 °C, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m,V_ = 10 m3/h Parameter m_ (kg/s) r (%) Charge 2.724 100.0 1. Outlet 1.258 46.2 2. Outlet 3.130 114.9 3. Outlet 0.852 31.3 4. Outlet 0 0
u (m/s) 0.088 0.073 0.181 0.049 0
m_ (kg/s) 2.714 1.238 2.160 1.886 0.096
r (%) 100.0 45.6 79.6 69.5 3.5
u (m/s) 0.089 0.072 0.125 0.109 0.005
so that in comparison to the charge system A a reduced suction occurs (approximately 13–14% less). This also
shows the representation of the mass flow rates in Figs. 10 and 11. Consequently, the application of inclined
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Fig. 10. Computed mass flow rates for the (a) charge system A, (b) charge system B with a charge temperature of 75 °C and a volume flow rate of 10 m3/h, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m.
Fig. 9. Vertical distribution of the pressure difference between the main pipe of the charge system and the storage tank. (a) tch = 75 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m; (b) tch = 65 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m.
branches leads to a clear reduction of the suction and a lower reduction of stratification. 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 tests. For the charge 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 114.9% 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
Fig. 11. Computed mass flow rates for the (a) charge system A, (b) charge system B with a charge temperature of 65 °C and a volume flow rate of 10 m3/h, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m.
third one. This shift becomes larger with increasing suction (cf. Figs. 10 and 11). For the charge 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. For the charge 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 Table 2 and Fig. 11):
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Table 2 Computed values of the fluid flows of the two charge systems (see Fig. 4). Construction
Charge system A
Charge system B
tch = 75 °C, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m, V_ = 10 m3/h Parameter m_ (kg/s) r (%) Charge 2.708 100.0 1. Outlet 0.699 25.8 2. Outlet 2.007 74.1 3. Outlet 1.400 51.7 4. Outlet 0 0
u (m/s) 0.088 0.041 0.117 0.081 0
m_ (kg/s) 2.708 0.325 1.575 1.458 0
r (%) 100.0 12.0 58.2 53.8 0
u (m/s) 0.088 0.019 0.091 0.085 0
tch = 65 °C, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m, V_ = 10 m3/h Parameter m_ (kg/s) r (%) Charge 2.724 100.0 1. Outlet 1.258 46.2 2. Outlet 3.130 114.9 3. Outlet 0.852 31.3 4. Outlet 0 0
u (m/s) 0.088 0.073 0.181 0.049 0
m_ (kg/s) 2.724 0.910 2.352 1.282 0
r (%) 100.0 33.4 86.3 47.1 0
u (m/s) 0.088 0.053 0.136 0.074 0
the 1.8-fold of the fluid flow in the third outlet for charge system B and the 3.7-fold for the charge system A. The reduced suction of the charge system B improves the charge behaviour and with it the build-up and the preservation of a stratification. The upper warm layer is preserved longer. The mixing in the storage tank is reduced by the lower velocities in the outlets. The 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 assumptions. The improvement potential for the introduced computation method lies here. 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 a reduced suction and to an 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. Acknowledgements This work was financially supported with resources of the Federal Ministry of environment, nature conservation and reactor security under the sign of promotion
0329271A. The authors are grateful for the support of the Project Management Organization Ju¨lich. References Ansys Inc., 2007. Ansys CFX 11.0. Canonsburg (USA). Andersen, E., Furbo, S., Hampel, M., Heidemann, W., Mu¨llerSteinhagen, H., 2008. Investigations on stratification devices for hot water heat stores. International Journal of Energy Research 32, 255–263. Go¨ppert, S., Urbaneck, T., Schirmer, U., Lohse, R., Platzer, B., 2008. Be- und Entladesyteme fu¨r thermische Schichtenspeicher: Teil ¨ berblick. Chemie Ingenieur Technik 80, 287–293. 1–U IAPWS, 1997. Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. Available at http://www.iapws.org. Idelchik, I.E., Steinberg, M.O. (Eds.), 1996. Handbook of Hydraulic Resistance, third ed. Begell House, New York. Lohse, R., Platzer, B., Urbaneck, T., Schirmer, U., Go¨ppert, S., Rauh, H., 2006. Optimierung von Be- und Entladesystemen mittels CFD. In: Research Centre Ju¨lich GmbH, Project Management Ju¨lich; Fraunhofer SOBIC (Hrsg.), state-of-the-art-workshop ‘‘Thermische Energiespeicherung”, proceedings, Freiburg, pp. 79–85. Lohse, R., Go¨ppert, S., Kunis, C., Urbaneck, T., Schirmer, U., Platzer, B., 2008. Be- und Entladesysteme fu¨r thermische Schichtenspeicher: Teil 2 – Untersuchungen des Beladeverhaltens. Chemie Ingenieur Technik 80, 935–943. Nikuradse, J., 1933. Stro¨mungsgesetze 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, 2086–2099. Sigloch, H., 2005. Technische Fluidmechanik. Springer, Berlin. Wagner, W., 1992. Stro¨mung und Druckverlust. 3. Aufl. Vogel (Kamprath–Reihe), Wu¨rzburg. Zigrang, D.J., Sylvester, N.D., 1982. Explicit approximations to the solution of Colebrook’s friction factor equation. AIChE Journal 28 (3), 514–515. Zurigat, Y.H., Ghajar, A.J., 2002. Heat transfer and stratification in sensible heat storage systems. In: Dincßer, I., Rosen, M.A. (Eds.), Thermal Energy Storage. Wiley, Chichester, pp. 259–302.
Solar Energy 83 (2009) 1578–1587 www.elsevier.com/locate/solener
New computation method for stratification pipes of solar storage tanks Stefan Go¨ppert *, Rolf Lohse, Thorsten Urbaneck, Ulrich Schirmer, Bernd Platzer, Philipp Steinert Department of Technical Thermodynamics, Chemnitz University of Technology, Reichenhainer Str. 70, 09126 Chemnitz, Germany Received 22 August 2008; received in revised form 11 May 2009; accepted 18 May 2009 Available online 11 June 2009 Communicated by: Associate Editor Halime Paksoy
Abstract The efficiency of low-flow solar systems is strongly influenced by the quality of the thermal stratification in the storage tank. The better a thermal stratification can be generated and maintained, the higher can be the yield of the solar system. Fluid mechanical charge systems are often used for this purpose, which 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) 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 for a simple charge system. The results of a constructive modification of the charge system reducing the sucking effect are discussed. The remaining quantitative differences result from the discrepancies between the non-ideal behaviour of the real fluid and the model assumptions and point out improvement potentials. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Solar storage tanks; Inlet stratifiers; Computation
1. Introduction A thermal stratification of the fluid makes sense for the storage of thermal energy in low-flow solar systems. Zurigat and Ghajar (2002) show in an overview 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 (Go¨ppert et al., 2008). Simple pipes with circular openings are widespread. Besides, there is also a lot of especially developed stratifiers, e.g. the respective patented charge systems of the ConSens *
Corresponding author. Tel.: +49 371 531 34749; fax: +49 371 531 800075. E-mail address: [email protected] (S. Go¨ppert). 0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.05.007
GmbH, Solvis KG and Sailer GmbH (Lohse et al., 2008; Andersen et al., 2008). 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. 1a) or colder water from the lower storage area (see Fig. 1b) is sucked. In the first case the usable temperature level decreases by cooling the upper area. In the second case the supply temperatures for the solar circuit rise by warming the lower area. The German
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Nomenclature a A c C d g h k l m m_ p r Re t u
area ratio () area (m2) specific heat capacity (kJ/kg/K) truncation criterion (Pa) diameter (m) acceleration due to gravity (m/s2) height (m) roughness (m) length (m) mass flow ratio () mass flow rate (kg/s) pressure (Pa) ratio (%) Reynolds number (–) temperature (°C) velocity (m/s)
V_ a q f k
volume flow rate (m3/s) departure angle (°) density (kg/m3) resistance coefficient (–) pipe friction factor (–)
Subscripts b bottom ch charging i number of respective junction mp main pipe st storage tank t top w water 1,2,3 locations
company Solvis is using check valves in their stratifiers to avoid such sucking effects. In this work only charge systems without check valves are considered. The following open questions arise from the explained mixing behaviour:
method and the underlying model offering this possibility are introduced. The algorithm resulting from the new model was implemented in MatLab. The time needed for an arithmetic calculation lies within few minutes.
How much fluid is sucked from the storage tank? Are there better and worse charge systems concerning the sucking? Is it possible to estimate the effect of constructive changes?
2. Computation method
Computations with CFD are costly and time-consuming. This is also true of experimental investigations. 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
2.1. Model The Bernoulli equation complemented by the pressure losses forms the basis of the new computational method: X q q f : ð1Þ p1 þ q1 gh1 þ 1 u21 ¼ p2 þ q2 gh2 þ 2 u22 1 þ 2 2 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. Vice versa a given inlet pressure causes a certain volume flow. In the developed algorithm the volume flow
Fig. 1. Sucking effects in fluid mechanical charge systems. (1) Sucked fluid flow, (2) charge flow. (a) Sucking of warmer water, (b) sucking of colder water.
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is given. 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 but has to be determined iteratively. 2.2. Pressure losses 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: l f¼k : d
ð2Þ
The pipe friction factor depends on the Reynolds number and on the roughness of the pipe. It can be computed with one of the following equations. For laminar flow the pipe friction factor depends only on the Reynolds number: k¼
f ¼ f ðRe; geometrical dimensions; kÞ:
ð7Þ
For longer segments, as for example curve or elbow, the losses of the pipe flow after Eq. (2) possibly have to be added to the resistance coefficients. Turbulent flow and hydraulically rough behaviour dominates 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. 2.3. Flow junction
64 : Re
ð3Þ
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): k¼
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:
0:309 ðlg Re 0:845Þ
2
for : Re
k < 65; d
ð4Þ
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).
hydraulic transitional range (Zigrang and Sylvester, 1982; explicit form of the equation according to Colebrook):
1 k 5:02 k 5:02 k 13 pffiffiffi ¼ 2 lg lg lg þ 3:7d Re 3:7d Re 3:7d Re k ð5Þ hydraulically rough (Nikuradse, 1933): k¼
1 ð2 lg dk þ 1:14Þ2
for : Re
k > 1300: d
ð6Þ
In the hydraulically rough range the pipe friction factor becomes independent of the Reynolds number.
Fig. 2. Flow relations in a t-piece of a fluid mechanical charge system. (a) Flow merging, (b) flow separation.
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The equations for flow merging are f2 ¼ 0:92ð1 mÞ2 þ mð1 mÞð2 aÞ cos a 1 1a m2 1:2 1 þ 0:8 1 2 cos a ; a a a ð8Þ 2
f3 ¼ 0:03ð1 mÞ þ mð1 mÞð2 aÞ h cos a i m2 1 þ 1:62 1 0:38ð1 aÞ ; a where m ¼ m_ 2 =m_ 3 and
a ¼ A2 =A3 :
The equations for flow separation are 1 a 2 cot f2 ¼ 0:95ð1 mÞ þ 0:4mð1 mÞ 1 þ a 2 a 0:4 0:1a ; þ m2 1:3 cot 0:3 þ 2 a2 2
ð9Þ ð10Þ ð11Þ
ð12Þ
f1 ¼ 0:03ð1 mÞ 0:2mð1 mÞ þ 0:35m2 ;
ð13Þ
where m ¼ m_ 2 =m_ 1
ð14Þ
and
a ¼ A2 =A1 :
ð15Þ
The continuity equation for both cases (with positive sign for flow merging and negative sign for flow separation) is: u3 q3 A3 ¼ u1 q1 A1 u2 q2 A2 :
ð16Þ
In addition, the law of conservation of energy must be taken into consideration for a flow merging in the view of mixing. Neglect of the kinetic energy yields: m_ 3 cw;3 t3 ¼ m_ 1 cw;1 t1 þ m_ 2 cw;2 t2 :
ð17Þ
In the case of outflow the boundary from vertical tube to tank (see position 2 in Fig. 2b) is used in the Bernoulli equation and the zetas of the junction and the branch are filled in. For flow merging, however, position 2 is in the tank because the velocity and therefore the static pressure at the opening are unknown. 2.4. Fluid properties The density, the specific heat capacity, and the viscosity of the fluid (here: water) are needed for the computation. All properties are determined in dependence on pressure and temperature being particularly important for the density. Therefore, the algorithms according to IAPWS (1997) are used. 2.5. Program sequence 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.
Fig. 3. Flow chart of the developed program.
Starting from this discharge opening, an initial value for the entrance pressure is estimated regarding only the hydrostatic pressure. In reverse direction pressures, temperatures, and mass flows along the charge system are computed now using the above equations. The condition Dp ¼ pmp;i pst;i Dploss ¼ 0
ð18Þ
is used for the last discharge opening, from which fluid flows into the tank. Since the initial value for the entrance pressure is determined without consideration of pressure losses, it is too
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low. Therefore, a negative Dp results. Now, the entrance pressure is increased gradually until a positive value is reached. Thus, two limit values are available for the entrance pressure. The iterative computation begins with the lower value. Then, the difference between the two limit values is halved in each step. The respective pressure is used as new lower or upper limit depending on whether Dp < 0 or Dp > 0. Using this iterative computation, Dp becomes smaller until the truncation criterion (here: C = 106 Pa) is fulfilled. At last, a tabulation of the computed data and diagrams are provided. 2.6. Restrictions 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 for the computations. 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 for pipe flow junctions or single resistances 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 and the resistance coefficients are taken into consideration individually. With the introduced computation only instantaneous constellations are considerable, however, no temporal charge.
Both charge systems are shown in Fig. 4. The main dimensions are the same for both variants. For charge system B the branches and the main pipe include an angle of 45° oppositely to the flow direction. The junctions, thereby, lie below the outlets. The outlets themselves lie on the same height for both variants. The charge behaviour was calculated for a volume flow rate of 10 m3/h and two different stratifications. Both given stratifications are shown in Fig. 5. The course follows a hyperbolic tangent. The temperature of the upper layer amounts to 80 °C and the temperature of the lower layer to 70 °C and 50 °C, respectively. 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 cover of the storage tank or alternatively at the water level for pressureless stores. The charge temperature is the middle temperature of the respective stratification.
3. Computations 3.1. Examined charge designs 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 (charge system A) as well as the ConSens charge system (charge system B). The charge system B contains a constructive modification of the charge 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.
Fig. 4. Examined charge designs.
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Fig. 5. Two given stratifications in the storage tank.
3.2. Comparison with CFD The fluid flow is investigated by means of three-dimensional CFD calculations using the commercial software package ANSYS CFX 11 (Ansys Inc., 2007). A SST k-x model extended for free convection is used to simulate the turbulent transport processes in the store. The properties for water are specified temperature-dependent. The cylindrical tank is set to 4 m in height as well as diameter providing a volume of approximately 50 m3. With a flow rate of 10 m3/h the store represents a short-term store. Fig. 6 shows a section of the grid. The whole grid comprises 530,000 elements. The computational model was validated against experimental data of a 0.6 m3 thermal energy store in earlier work (Lohse et al., 2008). The computed velocity field and temperature distribution for this experimental store are shown in Figs. 7a and 8a at the beginning of
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charge. In a further article a comparison of the new algorithm to experimental investigations with schlieren photography will follow. But this is beyond the scope of this article. Two comparative computations with CFD were carried out for the charge system A to validate the new algorithm. In Fig. 7b and c the respective velocity fields and in Fig. 8b and c the respective temperature distributions in the charge system and the tank are to be seen. The same behaviour occurs in the fluid flow as for the 0.6 m3 store. It only depends on the given stratification. This confirms the accuracy of the simulations for small and medium sized tanks. The numerical results of both computations are shown in Table 1. A positive mass flow stands for suction. A negative mass flow indicates that the fluid flows out of the charge system. 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 (Lohse et al., 2006, 2008). 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 Table 1. 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. Corresponding figures are shown in Lohse et al. (2008). 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. 3.3. Comparison of both charge systems
Fig. 6. Grid spacing in and nearby the charge system A.
These computations are carried out with the new method. 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. 9 the vertical distributions of this pressure difference are compared for the examined charge designs. The pressure differences over the branches cause the mass flows
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Fig. 7. Velocity field in the charge system A and the storage tank computed with CFD. (a) 0.6 m3 store, tch = 41.4 °C, V_ = 0.14 m3/h, tst,t = 58.7 °C, tst,b = 22.3 °C, h(tst = 41.4 °C) = 0.4 m; (b) 50 m3 store, tch = 75 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m; (c) 50 m3 store, tch = 65 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m.
out of or in the charge system. 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 the charge 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. 9b) 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 com-
pletely filled by the charge flow. The computed mass flow rates are shown in Fig. 10 or Fig. 11, respectively. The fourth junction as well as the bottom of the charge system is marked by small lines. Table 2 summarises the computed values of the in- and outflows, of the mean velocities in the outlets, and of the percentage ratios based on the primary inflow. According to Fig. 9, 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 clearly smaller for the charge system B,
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Fig. 8. Temperature distribution in the charge system A and the storage tank computed with CFD. (a) 0.6 m3 store, tch = 41.4 °C, V_ = 0.14 m3/h, tst,t = 58.7 °C, tst,b = 22.3 °C, h(tst = 41.4 °C) = 0.4 m; (b) 50 m3 store, tch = 75 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m; (c) 50 m3 store, tch = 65 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m. Table 1 Comparison of fluid flows computed with MatLab and CFD for the charge system A (see Fig. 4a). Method
MatLab
CFD
tch = 75 °C, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m, V_ = 10 m3/h Parameter m_ (kg/s) r (%) Charge 2.708 100.0 1. Outlet 0.699 25.8 2. Outlet 2.007 74.1 3. Outlet 1.400 51.7 4. Outlet 0 0
u (m/s) 0.088 0.041 0.117 0.081 0
m_ (kg/s) 2.690 0.602 1.520 1.772 0
r (%) 100.0 22.4 56.5 65.9 0
u (m/s) 0.088 0.035 0.088 0.103 0
tch = 65 °C, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m,V_ = 10 m3/h Parameter m_ (kg/s) r (%) Charge 2.724 100.0 1. Outlet 1.258 46.2 2. Outlet 3.130 114.9 3. Outlet 0.852 31.3 4. Outlet 0 0
u (m/s) 0.088 0.073 0.181 0.049 0
m_ (kg/s) 2.714 1.238 2.160 1.886 0.096
r (%) 100.0 45.6 79.6 69.5 3.5
u (m/s) 0.089 0.072 0.125 0.109 0.005
so that in comparison to the charge system A a reduced suction occurs (approximately 13–14% less). This also
shows the representation of the mass flow rates in Figs. 10 and 11. Consequently, the application of inclined
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Fig. 10. Computed mass flow rates for the (a) charge system A, (b) charge system B with a charge temperature of 75 °C and a volume flow rate of 10 m3/h, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m.
Fig. 9. Vertical distribution of the pressure difference between the main pipe of the charge system and the storage tank. (a) tch = 75 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m; (b) tch = 65 °C, V_ = 10 m3/h, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m.
branches leads to a clear reduction of the suction and a lower reduction of stratification. 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 tests. For the charge 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 114.9% 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
Fig. 11. Computed mass flow rates for the (a) charge system A, (b) charge system B with a charge temperature of 65 °C and a volume flow rate of 10 m3/h, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m.
third one. This shift becomes larger with increasing suction (cf. Figs. 10 and 11). For the charge 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. For the charge 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 Table 2 and Fig. 11):
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Table 2 Computed values of the fluid flows of the two charge systems (see Fig. 4). Construction
Charge system A
Charge system B
tch = 75 °C, tst,t = 80 °C, tst,b = 70 °C, h(tst = 75 °C) = 1.3 m, V_ = 10 m3/h Parameter m_ (kg/s) r (%) Charge 2.708 100.0 1. Outlet 0.699 25.8 2. Outlet 2.007 74.1 3. Outlet 1.400 51.7 4. Outlet 0 0
u (m/s) 0.088 0.041 0.117 0.081 0
m_ (kg/s) 2.708 0.325 1.575 1.458 0
r (%) 100.0 12.0 58.2 53.8 0
u (m/s) 0.088 0.019 0.091 0.085 0
tch = 65 °C, tst,t = 80 °C, tst,b = 50 °C, h(tst = 65 °C) = 1.3 m, V_ = 10 m3/h Parameter m_ (kg/s) r (%) Charge 2.724 100.0 1. Outlet 1.258 46.2 2. Outlet 3.130 114.9 3. Outlet 0.852 31.3 4. Outlet 0 0
u (m/s) 0.088 0.073 0.181 0.049 0
m_ (kg/s) 2.724 0.910 2.352 1.282 0
r (%) 100.0 33.4 86.3 47.1 0
u (m/s) 0.088 0.053 0.136 0.074 0
the 1.8-fold of the fluid flow in the third outlet for charge system B and the 3.7-fold for the charge system A. The reduced suction of the charge system B improves the charge behaviour and with it the build-up and the preservation of a stratification. The upper warm layer is preserved longer. The mixing in the storage tank is reduced by the lower velocities in the outlets. The 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 assumptions. The improvement potential for the introduced computation method lies here. 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 a reduced suction and to an 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. Acknowledgements This work was financially supported with resources of the Federal Ministry of environment, nature conservation and reactor security under the sign of promotion
0329271A. The authors are grateful for the support of the Project Management Organization Ju¨lich. References Ansys Inc., 2007. Ansys CFX 11.0. Canonsburg (USA). Andersen, E., Furbo, S., Hampel, M., Heidemann, W., Mu¨llerSteinhagen, H., 2008. Investigations on stratification devices for hot water heat stores. International Journal of Energy Research 32, 255–263. Go¨ppert, S., Urbaneck, T., Schirmer, U., Lohse, R., Platzer, B., 2008. Be- und Entladesyteme fu¨r thermische Schichtenspeicher: Teil ¨ berblick. Chemie Ingenieur Technik 80, 287–293. 1–U IAPWS, 1997. Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. Available at http://www.iapws.org. Idelchik, I.E., Steinberg, M.O. (Eds.), 1996. Handbook of Hydraulic Resistance, third ed. Begell House, New York. Lohse, R., Platzer, B., Urbaneck, T., Schirmer, U., Go¨ppert, S., Rauh, H., 2006. Optimierung von Be- und Entladesystemen mittels CFD. In: Research Centre Ju¨lich GmbH, Project Management Ju¨lich; Fraunhofer SOBIC (Hrsg.), state-of-the-art-workshop ‘‘Thermische Energiespeicherung”, proceedings, Freiburg, pp. 79–85. Lohse, R., Go¨ppert, S., Kunis, C., Urbaneck, T., Schirmer, U., Platzer, B., 2008. Be- und Entladesysteme fu¨r thermische Schichtenspeicher: Teil 2 – Untersuchungen des Beladeverhaltens. Chemie Ingenieur Technik 80, 935–943. Nikuradse, J., 1933. Stro¨mungsgesetze 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, 2086–2099. Sigloch, H., 2005. Technische Fluidmechanik. Springer, Berlin. Wagner, W., 1992. Stro¨mung und Druckverlust. 3. Aufl. Vogel (Kamprath–Reihe), Wu¨rzburg. Zigrang, D.J., Sylvester, N.D., 1982. Explicit approximations to the solution of Colebrook’s friction factor equation. AIChE Journal 28 (3), 514–515. Zurigat, Y.H., Ghajar, A.J., 2002. Heat transfer and stratification in sensible heat storage systems. In: Dincßer, I., Rosen, M.A. (Eds.), Thermal Energy Storage. Wiley, Chichester, pp. 259–302.