Effect of Step-Change Radiation Flux on Dynamic Characteristics in Tower Solar Cavity Receiver

Abstract

The heat flux on the inner surface of the tower solar thermal power plant system will show the characteristics of noncontinuous step change, especially in nonnormal and transient weather conditions, which may result in a continuous dynamic variation of the characteristic parameters. Therefore, the research of dynamic characteristics plays a very important role in the operation and the control safely in solar cavity receiver system. In this paper, based on the noncontinuous step change of radiation flux, a non-linear dynamic model is constructed to obtain the effects of the non-continuous step change radiation flux and step change feed water flow on the receiver performance by sequential modular approach. The subject investigated in our study is a 1 MW solar power station constructed in Yanqing county, Beijing, China. This study has obtained the dynamic responses of the characteristic parameters in the cavity receiver such as drum pressure, drum water level, main steam flow, and main steam enthalpy under step change radiation flux. And the influence of step-change feed water flow to the dynamic characteristics has also been analyzed. The results could provide general guidance for security operation and control in solar cavity receiver system.

1. Introduction

The solar cavity receiver is an important light energy to thermal energy convector in the tower solar thermal power plant system. Extensive research on the solar tower power plant principle has been conducted in America, Germany, Spain, France, Italy, the former Soviet Union, and Japan ever since it was put forward in the early 1970s. As a key listed project of the 11th Five-Year Plan of China National Hi-Tech R&D (863 Plan), the first 1 MW solar power tower system located in Beijing has been sponsored and is under construction now. In addition, the solar cavity receiver is an important light energy to thermal energy convector in the tower solar thermal power plant system, which is apt to be operated under the condition of high-density, ever-changing heat radiation flux frequently [1]. The heat flux may result in a continuous variation of the characteristic parameters, which will seriously affect the stability and safe operation of the solar cavity receiver. And with the improvement of cycling parameters, these problems will be more prominent.

A volume of research has been performed on high-temperature and high-pressure tower solar cavity receiver at home and abroad, and it mainly involved the structural design of cavity receiver, the thermal performance simulation, the system efficiency evaluation, and optimization design of the heliostat field [2, 3]. However, little attention has been focused on the instability of the steam-water system caused by noncontinuous heat flux in the cavity. Up to now, the inherent mechanism of dynamic characteristics and the control strategies of solar cavity receiver have not been clearly mastered.

In this study, in order to obtain the effects of the noncontinuous step change radiation flux on the receiver performance, a nonlinear dynamic model under step change radiation flux is constructed based on the distributed parameters, two-phase flow in the steam-water system, and the noncontinuous step change of radiation flux. This study aims to present the dynamic responses of the parameters in the cavity receiver such as drum pressure, drum water level, main steam flow, and main steam enthalpy under noncontinuous step change radiation flux. Meanwhile, the feed water flow is also one of the influencing factors on the receiver performance, so the influence law of step-change feed water flow to the dynamic characteristics in the receiver was also analyzed. The results of this study could provide general guidance for the design of cavity receivers and identification of the operational strategy of the solar thermal power tower plant.

2. The Steam-Water System

The subject investigated in our study is a 1 MW solar power station constructed in Yanqing county, Beijing, China. The solar cavity receiver has a hexagonal prism shape. The profile of the cavity receiver is shown in Figure 1. Solar radiation enters through the front face and is absorbed by the interior walls of the cavity. As shown in Figure 1, the boiling zone has three panels of vertical pipes welded together to form a membrane wall, and two panels are at the sides of the cavity and one is at the center. The other two faces are coated with insulation, which can decrease the absorbing energy. Evaporation surfaces are arranged in both sides and the center of the cavity, and superheat surfaces are arranged in the sides of the cavity. In order to achieve steam-water separation and stabilize the steam-water system, drum and circulating pump were designed in the system. The circulating flowchart of the steam-water system is shown in Figure 2. Spray desuperheater is arranged between the superheaters in order to obtain acceptable superheated steam. The superheated steam temperature designed can reach 410°C.

Figure 1:

Profile of cavity receiver.

Figure 2:

Steam and water system of cavity receiver.

3. Mathematical Model

In this paper, in order to accurately obtain variable law of the dynamic characteristic, lumped parameter method and sequential modular approach are adopted to build a nonlinear dynamic mathematical model of the steam-water system in the solar cavity receiver. According to sequential modular approach, the steam-water system of the cavity receiver can be simplified into several typical parts based on modularization modeling method. This method can not only improve the model's accuracy but also reduce the complexity in model establishment and numerical solution. The steam-water system is composed of evaporation zone and superheat zone. And evaporation zone is simplified into several typical parts including downcomer, water-wall metal, water wall, steam-water catheter, and drum which are coupled by pressure variation and state parameters. In particular, the water-wall surface is divided into supercooled-water section and two-phase section, and the convective heat transfer coefficient is determined by the flow pattern in each section. And mathematics description of drum pressure and drum water level is analyzed and derived considering various influencing factors. A nonlinear dynamic mathematical model for the cavity receiver based on the laws of mass conservation, energy conservation, and momentum conservation, which give a comprehensive consideration of flash or condensation in the two-phase flow, is proposed. Furthermore, superheat zone is simplified into two typical parts including superheat tube and the superheat tube metal. The schematic diagram of dynamic parameters in steam-water system is shown in Figure 3.

Figure 3:

Schematic diagram of dynamic parameters.

3.1. Evaporation Zone Model

According to the specific structure and working process of the cavity receiver, the dynamic mathematical model for these typical modules, including downcomer, water-wall, steam-water catheter, and drum, is built based on the distributed parameters, two-phase flow in steam-water system.

3.1.1. Downcomer Module

Mass conservation equation is as follows:

$D_x=D_{xj}.$

(1)

Energy conservation equation is as follows:

$\frac{d\left(V_{xj}{\rho }^{\prime }{H}_{xj}+M_{jxj}{C}_j{T}_j\right)}{d\tau }=D_x{H}_x-D_{xj}{H}_{xj},$

(2)

where D _x and D _xj are the inlet and outlet mass flow of the downcomer, V _xj is the volume of the downcomer, ρ′ is the density of saturated water, M _jxj is the mass of the downcomer metal, C _j is the specific heat capacity of metal pipe, T _j is the temperature of downcomer metal, and H _x and H _xj are the inlet and outlet enthalpy in the downcomer.

3.1.2. Water-Wall Module

The change of radiation flux will result in a variation of the temperature of the metal wall, which may cause thermal inertia of the heat absorption [4], so metal wall should be considered as an independent link.

Energy conservation equations of the water-wall metal are as follows:

$\begin{array}{c}{M}_{jlb}{C}_j\frac{d{T}_{bw}}{d\tau }=Q-Q_{zf}-Q_{fs}-Q_{dl},\\ Q_{zf}=hA\left(T_{bw}-T\right),\end{array}$

(3)

where M _jlb is the mass of the water-wall tube metal, T _bw is the temperature of tube metal, Q is the solar radiation flux, Q _zf is the heat absorption of working fluid in the water wall, Q _fs is the loss of radiant heat, Q _dl is the loss of convective heat, and h is the convective heat transfer coefficient of the evaporation surface.

Dynamic equations of the water wall, including mass conservation equation, energy conservation equation, mass conservation equation for steam, and mass conservation equation for water, based on convective heat transfer between tube metal and working fluid, which give a comprehensive consideration of flash and condensation caused by pressure change in the two-phase flow, are built as follows:

$\begin{array}{c}\frac{d\left(V^{\prime }{\rho }^{\prime }+V^{\mathrm{\prime \prime }}{\rho }^{\mathrm{\prime \prime }}\right)}{d\tau }=D_{xj}-D_{lb},\\ \frac{d\left(V^{\prime }{\rho }^{\prime }{H}^{\prime }+V^{\mathrm{\prime \prime }}{\rho }^{\mathrm{\prime \prime }}{H}^{\mathrm{\prime \prime }}\right)}{d\tau }=D_{xj}{H}_{xj}-D_{lb}{H}_{lb}+Q_{zf},\\ \frac{d\left(V^{\mathrm{\prime \prime }}{\rho }^{\mathrm{\prime \prime }}\right)}{d\tau }=D_{zf}+D_{sz}-D_{lb}x,\\ \frac{d\left(V^{\prime }{\rho }^{\prime }\right)}{d\tau }=D_{xj}-D_{lb}\left(\mathrm{1}-x\right)-D_{zf}-D_{sz},\end{array}$

(4)

where V′ is the volume of water in the water wall, V^″ is the volume of steam in the water wall, H′ and H^″ are enthalpy of saturated water and steam, D _lb is the outlet mass flow of water-wall tube, x is the mass rate of vapor content in the outlet of water wall tube; and D _sz is the mass of flash or condensation in water-wall, within this model we thus derive the following:

$D_{\text{sz}}=-((\left({\rho }^{\prime }\frac{\partial H^{\prime }}{\partial P}+\frac{r{\rho }^{\mathrm{\prime \prime }}}{{\rho }^{\prime }-{\rho }^{\mathrm{\prime \prime }}}\frac{\partial {\rho }^{\prime }}{\partial P}\right)V^{\prime }+\left({\rho }^{\mathrm{\prime \prime }}\frac{\partial H^{\mathrm{\prime \prime }}}{\partial P}+\frac{r{\rho }^{\prime }}{{\rho }^{\prime }-{\rho }^{\mathrm{\prime \prime }}}\frac{\partial {\rho }^{\mathrm{\prime \prime }}}{\partial P}\right)V^{\mathrm{\prime \prime }})\times {\left(H^{\mathrm{\prime \prime }}-H^{\prime }\right)}^{-1})\times \frac{\partial P}{\partial \tau },$

(5)

where r is the latent heat of vaporization.

In our model, water-wall surface is divided into supercooled-water section and two-phase section, and the length of two-phase section y _rs can be calculated as y _rs = D _xj (H′ – H _xj )/Q _zf . The convective heat transfer coefficient between tube wall and working fluid is determined by the physical parameters and the flow pattern of the working fluid in each section. The convective heat transfer coefficient of the evaporation surfaces can be calculated as single-phase fluid forced flow and nucleate heat transfer coefficient in two-phase fluid forced flow in this model.

The Dittus-Boelte formula [5] given below is used to calculate the heat transfer coefficient h in single-phase fluid forced flow directly:

$h=\mathrm{0.023}\frac{\lambda }{d}\text{R}{\text{e}}^{\mathrm{0.8}}\text{P}{\text{r}}^{\mathrm{0.4}},$

(6)

where λ is the heat conduction coefficient of the saturated water, Re is the Reynolds number, Pr is prenatal number, and d is the equivalent diameter of the heating surface.

Nucleate heat transfer coefficient in two-phase fluid forced flow can be computed by the Chen formula [5] as follows:

$\begin{array}{c}h=h_{NB}+h_c,\\ h_{NB}=\mathrm{0.00122}\left[\frac{\mathrm{0.79}{\lambda }^{\prime }{C_p^{\prime }}^{\mathrm{0.45}}{{\rho }^{\prime }}^{\mathrm{0.49}}}{{\sigma }^{\mathrm{0.5}}{{\mu }^{\prime }}^{\mathrm{0.29}}{\gamma }^{\mathrm{0.24}}{{\rho }^{\mathrm{\prime \prime }}}^{\mathrm{0.49}}}\right]\mathrm{\Delta }{t}_{\mathrm{sat}}^{\mathrm{0.24}}\mathrm{\Delta }{p}_{\mathrm{sat}}^{\mathrm{0.75}}s,\\ s={\left[\mathrm{1}+\mathrm{2.53}\times \mathrm{1}{\mathrm{0}}^{-\mathrm{6}}{\left(\mathrm{Re}\right)}_{{\mathrm{\hspace{0.17em}\hspace{0.17em}}}_{TP}}^{\mathrm{1.17}}\right]}^{-\mathrm{1}},\\ {\left(\mathrm{Re}\right)}_{\text{TP}}=\left[\frac{D_{lb}\left(1-x\right)d}{{\mu }^{\prime }}\right]F^{1.25},\\ X={\left(\frac{\mathrm{1}-x}{x}\right)}^{\mathrm{0.9}}{\left(\frac{{\rho }^{\mathrm{\prime \prime }}}{{\rho }^{\prime }}\right)}^{\mathrm{0.05}}{\left(\frac{{\mu }^{\prime }}{{\mu }^{\mathrm{\prime \prime }}}\right)}^{\mathrm{0.1}},\\ \frac{\mathrm{1}}{X}\le \mathrm{0.1},\hspace{1em}\hspace{1em}F=\mathrm{1.0},\\ \frac{\mathrm{1}}{X}>\mathrm{0.1},\hspace{1em}\hspace{1em}F=\mathrm{2.35}{\left(\frac{\mathrm{1}}{X}+\mathrm{0.213}\right)}^{\mathrm{0.736}}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{\hspace{0.17em}\hspace{0.17em}}\\ h_c=0.023\frac{{\lambda }^{\prime }}{d}{\left[\frac{D_{lb}\left(1-x\right)d}{{\mu }^{\prime }}\right]}^{0.8}{\left[\frac{{\mu }^{\prime }{C}_p^{\prime }}{{\lambda }^{\prime }}\right]}^{0.4}F,\end{array}$

(7)

where h _NB and h _c are heat transfer coefficient in bubble state boiling and convective heat transfer, σ is interfacial force coefficient, γ is the latent heat of vaporization, μ is viscosity of working fluid, Δt _sat is overheat rate of the pipe wall, Δp _sat is the saturated pressure difference corresponding to Δt _sat , s is the inhibition coefficient of bubble state boiling, x is the mass rate of vapor content, F is the coefficient relevant to the Martinelli number, (Re)_TP is the two-phase Reynolds number, and X is the Martinelli number.

3.1.3. Steam-Water Catheter Module

Dynamic equations of the steam-water catheter module, including mass conservation equation, energy conservation equation, mass conservation equation for steam, and mass conservation equation for water, which give a comprehensive consideration of flash and condensation caused by pressure change in the two-phase flow, are built as follows:

$\begin{array}{c}\frac{d\left(V_{qs}^{\prime }{\rho }^{\prime }+V_{qs}^{\prime \prime }{\rho }^{\prime \prime }\right)}{d\tau }=D_{lb}-D_{qs},\\ \frac{d\left(V_{qs}^{\prime }{\rho }^{\prime }{H}^{\prime }+V_{qs}^{\prime \prime }{\rho }^{\prime \prime }{H}^{\prime \prime }+M_{jqs}{C}_j{T}_{bh}\right)}{d\tau }=D_{lb}{H}_{lb}-D_{qs}{H}_{qs},\\ \frac{d\left(V_{qs}^{\prime \prime }{\rho }^{\prime \prime }\right)}{d\tau }=D_{lb}x+D_{szqs}-D_{qs}{x}_{qs},\\ \frac{d\left(V_{qs}^{\prime }{\rho }^{\prime }\right)}{d\tau }=D_{lb}\left(1-x\right)-D_{qs}\left(1-x_{qs}\right)-D_{szqs},\end{array}$

(8)

where V _qs ′ is the water volume in the steam-water catheter, V _qs ^″ is the steam volume in the steam-water catheter, D _qs is the outlet mass flow of steam-water catheter tube, x _qs is the mass rate of vapor content of the outlet of steam-water catheter tube, and D _szqs is the mass of flash or condensation of two-phase flow in steam-water catheter; within this model we thus derive the following:

$D_{szqs}=-(\left({\rho }^{\prime }\frac{\partial H^{\prime }}{\partial P}+\frac{r{\rho }^{\prime \prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}\frac{\partial {\rho }^{\prime }}{\partial P}\right)V_{qs}^{\prime }+\left({\rho }^{\prime \prime }\frac{\partial H^{\prime \prime }}{\partial P}+\frac{r{\rho }^{\prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}\frac{\partial {\rho }^{\prime \prime }}{\partial P}\right)V_{qs}^{\prime \prime }+M_{jqs}{C}_j\frac{\partial T_{bh}}{\partial P})\frac{\left(\partial P/\partial \tau \right)}{\left(H^{\prime \prime }-H^{\prime }\right)}.$

(9)

3.1.4. Drum Module

Dynamic equations of the drum module, including mass conservation equation, energy conservation equation, mass conservation equation for steam, and mass conservation equation for water, which give a comprehensive consideration of flash and condensation caused by pressure change in the drum, are built as follows:

$\begin{array}{c}\frac{d\left(V_{qb}^{\prime }{\rho }^{\prime }{H}^{\prime }+V_{qb}^{\prime \prime }{\rho }^{\prime \prime }{H}^{\prime \prime }+M_{jqb}{C}_j{T}_{bh}\right)}{d\tau }\hspace{0.17em}=D_{gs}{H}_{gs}+D_{qs}{H}_{qs}-D_{qb}{H}^{\prime \prime }-D_x{H}_x-D_{pw}{H}^{\prime },\\ \frac{d\left(V_{qb}^{\prime }{\rho }^{\prime }+V_{qb}^{\prime \prime }{\rho }^{\prime \prime }\right)}{d\tau }=D_{gs}+D_{qs}-D_{qb}-D_x-D_{pw},\\ \frac{d\left(V_{qb}^{\prime \prime }{\rho }^{\prime \prime }\right)}{d\tau }=D_{qs}{x}_{qs}-D_{qb}+D_{szqb},\\ \frac{d\left(V_{qb}^{\prime }{\rho }^{\prime }\right)}{d\tau }=D_{gs}+D_{qs}\left(1-x_{qs}\right)-D_x-D_{pw}-D_{szqb},\end{array}$

(10)

where M _jqb is the mass of drum metal, V _qb ′ and V _qb ^″ are the volume of water and steam in the drum, D _qb is mass flow of main steam, D _pw is pollutant quantity of the drum; and D _szqs is the mass of flash or condensation in the drum, within this model we thus derive the following:

$D_{szqb}=-(\left({\rho }^{\prime }\frac{\partial H^{\prime }}{\partial P}+\frac{r{\rho }^{\prime \prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}\frac{\partial {\rho }^{\prime }}{\partial P}\right)V_{qb}^{\prime }\hspace{0.17em}+\left({\rho }^{\prime \prime }\frac{\partial H^{\prime \prime }}{\partial P}+\frac{r{\rho }^{\prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}\frac{\partial {\rho }^{\prime \prime }}{\partial P}\right)V_{qb}^{\prime \prime }\hspace{0.17em}+M_{jqb}{C}_j\frac{\partial T_{bh}}{\partial P})\frac{\left(\partial P/\partial \tau \right)}{\left(H^{\prime \prime }-H^{\prime }\right)}.$

(11)

The dynamic variable law of the state parameters in each module can be obtained by solving these nonlinear equations and partial differential equations above. The drum pressure is seen as a lumped parameter, so the influencing factors in all modules should be considered in the derivation of pressure dynamic respond equation [6]. The dynamic respond equation of drum pressure is as follows:

$\frac{dP}{d\tau }=[Q_{zf}+\left(\frac{r{\rho }^{\prime \prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}-H_{qh}\right)D_{gs}\hspace{0.17em}-\frac{r{\rho }^{\prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}{D}_{qb}-\frac{r{\rho }^{\prime \prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}{D}_{lp}]\hspace{0.17em}\times ([\left({\rho }^{\prime }\frac{\partial H^{\prime }}{\partial P}+\frac{r{\rho }^{\prime \prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}\frac{\partial {\rho }^{\prime }}{\partial P}\right)V{V}^{\prime }\hspace{0.17em}+\left({\rho }^{\prime \prime }\frac{\partial H^{\prime \prime }}{\partial P}+\frac{r{\rho }^{\prime }}{{\rho }^{\prime }-{\rho }^{\prime \prime }}\frac{\partial {\rho }^{\prime \prime }}{\partial P}\right){VV}^{\prime \prime }\hspace{0.17em}+\left({\rho }^{\prime }\frac{d{H}_{xj}}{dP}+H_{xj}\frac{d{\rho }^{\prime }}{dP}\right)V_{xj}\hspace{0.17em}{+\left(M_{jxj}+M_{jqs}+M_{jqb}\right)C_j\frac{\partial T_{bh}}{\partial P}])}^{-1}.$

(12)

The drum water level is determined by the water cubage in the drum and steam cubage in water, that is, $(\partial h/\partial \tau )S_{qb}=(\partial V_{qb}^{\prime }/\partial \tau )+(\partial V_{sx}^{\prime \prime }/\partial \tau )$ . According to the specific structure of the drum, we can obtain the dynamic respond equation of drum water level given in the following:

$\frac{dh}{d\tau }=\frac{\left(D_{gs}-D_{qb}-D_{lp}\right)}{S_{qb}\left({\rho }^{\prime }-{\rho }^{\prime \prime }\right)}\hspace{0.17em}-\frac{\left(V_{qb}^{\prime }\left(\partial {\rho }^{\prime }/\partial P\right)+V_{qb}^{\prime \prime }\left(\partial {\rho }^{\prime \prime }/\partial P\right)\right)}{S_{qb}\left({\rho }^{\prime }-{\rho }^{\prime \prime }\right)}\frac{dP}{d\tau }\hspace{0.17em}-\frac{\partial M_{xh}/\partial \tau }{S_{qb}\left({\rho }^{\prime }-{\rho }^{\prime \prime }\right)}+\frac{1}{S_{qb}}\frac{\partial V_{sx}^{\prime }}{\partial \tau },$

(13)

where H _qh is the enthalpy difference, VV′ is total water volume in the evaporation zone, which can be calculated as VV′ = V _xj + V′ + V _qs ′ + V _qb ′, VV^″ is total steam volume in the evaporation zone, which can be calculated as VV^″ = V^″ + V _qs ^″ + V _qb ^″, M _xh is total mass of working fluid in the downcomer module, water-wall module, and steam-water catheter module, V _sx ^″ is steam cubage in water in the drum, and S _qb is the cross-section area of the drum water level, which is determined by the structure of the drum.

3.2. Superheated Zone Model

The modeling method of superheater metal wall is similar to that of the water-wall metal module above. As for the superheating surface, a chain structure dynamic mathematical model [7], which gives a comprehensive consideration of model precision, is established, and the superheating surface is divided into 15 segments.

Energy conservation equation is as follows:

$\frac{d\left(V_{gr}{\rho }_{gr}e\right)}{d\tau }=D_{qb}{H}_{qb}+Q_{gr}-D_{gr}{H}_{gr}.$

(14)

Mass conservation equation is as follows:

$V_{gr}\frac{d{\rho }_{gr}}{d{P}_{gr}}\frac{d{P}_{gr}}{d\tau }=D_{qb}-D_{gr}.$

(15)

We can obtain the dynamic respond equations of superheater outlet pressure and superheater outlet steam temperature as shown in (16) and (17):

$\frac{d{P}_{gr}}{d\tau }=(\phantom{-\left(H_{gr}+{\rho }_{gr}{c}_p\frac{\partial T_{gr}}{\partial \rho }\right)}{Q}_{gr}+\left(D_{qb}{H}_{qb}-D_{gr}{H}_{gr}\right)\hspace{0.17em}-\left(H_{gr}+{\rho }_{gr}{c}_p\frac{\partial T_{gr}}{\partial \rho }\right)\left(D_{qb}-D_{gr}\right))\hspace{0.17em}\times {\left(V_{gr}\left({\rho }_{gr}{c}_p\frac{\partial T_{gr}}{\partial P_{gr}}-1\right)\right)}^{-1},$

(16)

$\frac{d{T}_{gr}}{d\tau }=(\phantom{-\left(H_{gr}+{\rho }_{gr}{c}_p\frac{\partial T_{gr}}{\partial \rho }\right)}{Q}_{gr}+\left(D_{qb}{H}_{qb}-D_{gr}{H}_{gr}\right)-\left({\rho }_{gr}{c}_p\frac{\partial P_{gr}}{\partial \rho }-H_{gr}\right)\left(D_{qb}-D_{gr}\right))\hspace{0.17em}{\times \left(V_{gr}\left({\rho }_{gr}{c}_p-\frac{\partial P_{gr}}{\partial T_{gr}}\right)\right)}^{-1},$

(17)

where e is the internal energy of superheated steam, ρ _gr is the density of superheated steam, P _gr is superheater outlet pressure, Q _gr is the exchanged heat between steam and metal pipe, V _gr is volume of the superheated tube, H _gr is superheater outlet temperature, D _gr is the mass flow of superheated steam, and c _p is the specific heat capacity of superheated steam.

4. Simulation Results

In order to master the influence law of noncontinuous radiation flux on the receiver performance in nonnormal weather conditions, a numerical study on the basis of the nonlinear dynamic mathematical model, which can be solved by the Runge-Kutta method, is carried out focusing on the cavity receiver of 1 MW solar power station constructed in Yanqing county, Beijing. The dynamic responses of the characteristic parameters of the cavity receiver under step change radiation flux and step change feed water flow have been obtained in this paper.

4.1. Step Increase of Radiation Flux

The step change of radiation flux in nonnormal and transient weather conditions may result in a continuous variation of the characteristic parameters in the solar cavity receiver. So it will seriously affect the stability and safe operation of the solar cavity receiver. The designed value of radiation flux in the receiver is 100.5 kw/m². The dynamic responses of characteristic parameters in the cavity receiver, such as water-wall outlet dryness, drum pressure, main steam flow, superheater outlet pressure, drum water level, and superheater outlet enthalpy, are shown in Figures 4 (a)–4 (f) when there is a step increase by 10%, 20%, and 30% of solar radiation flux.

Figure 4:

The dynamic responses of characteristic parameters with step increase of radiation flux.

When there is a step increase of solar radiation flux, the water-wall outlet dryness first increases rapidly and then reaches the steady state about 350 s later than the step increase of radiation flux, and the rate of increase is from fast to slow, as shown in Figure 4 (a). This is because the water-wall outlet dryness depends on both radiation flux and the flash or condensation caused by pressure variation in two-phase flow. As shown in Figures 4 (b)–4 (d), the drum pressure increases regardless of the increased radiation flux, and the superheater outlet pressure increases more slowly than that of drum pressure, so there is a very rapid increase of the main steam flow due to the increase of pressure drop in superheater. The main steam flow D _qb has a negative feedback on the drum pressure [8, 9], and the increase of D _qb can slow down the increase rate of pressure and make it become stable. Due to the pressure increase and condensation caused by increasing pressure, the main steam flow D _qb tends to be stable about 400 s later than the step change.

The dynamic response of drum water level is shown in Figure 4 (e). It shows the phenomenon of false water level in the case of a sudden increase in radiation flux. Based on dynamic analysis and the simulation of water level model, this paper indicates that the changing mass storage in evaporation area and the steam cubage in water are two important factors of false water level. On the one hand, the steam cubage in water and pressure will increase along with the heat absorption in evaporation area. On the other hand, the length of single-phase section in water wall and the working fluid density will decrease, which can result in a decrease of mass storage in evaporation area. There emerges a relatively serious phenomenon indicating a false water level as shown in Figure 4 (e), and the water in the drum will dry up, respectively, at 3250 s, 1716 s, and 1223 s when there is a step increase by 10%, 20%, and 30% of solar radiation flux. So necessary measures should be taken in order to make the water level stable.

The dynamic response of superheater outlet enthalpy is shown in Figure 4 (f). The superheater outlet enthalpy first increases rapidly and then decreases and stabilizes gradually to a certain value. It follows from (17) that the main cause of superheater outlet enthalpy change is not only the function of received solar energy in the superheater but also the superheater steam flow. The rate of steam generation is slower than the change of solar radiation flux. Thus, the above-mentioned result will appear, and the superheater outlet steam enthalpy tends to be stable about 400 s later than the step change.

4.2. Step Decrease of Radiation Flux

The occlusion of cloud layer in nonnormal and transient weather conditions may result in a step decrease of radiation flux in the receiver. The dynamic responses of characteristic parameters in the cavity receiver, such as water-wall outlet dryness, drum pressure, main steam flow, superheater outlet pressure, drum water level, and superheater outlet enthalpy, are shown in Figures 5 (a)–5 (f) when there is a step decrease by 10%, 20%, and 30% of solar radiation flux.

Figure 5:

The dynamic responses of characteristic parameters with step decrease radiation flux.

As shown in Figures 5 (a)–5 (d), the water-wall outlet dryness first decreases rapidly and then reaches the steady state. The drum pressure, the superheater outlet pressure, and the main steam flow decrease because of the increased radiation flux, and the rate of decrease is from fast to slow. Due to the pressure decrease and flash caused by decreasing pressure, the main steam flow D _qb tends to be stable about 400 s later than the step change.

The dynamic response of drum water level is shown in Figure 5 (e). There emerges a relatively serious phenomenon of indicating a false water level at the beginning, and then the water will fulfill the drum at 3002 s, 1674 s, and 1209 s when there is a step decrease by 10%, 20%, and 30% of solar radiation flux.

The dynamic response of superheater outlet steam enthalpy is shown in Figure 5 (f). The superheater outlet steam enthalpy first decreases rapidly to a certain value and then increases to a stable value. As is analyzed above, the superheater steam outlet enthalpy depends on both the main steam flow D _qb and the heat absorption of steam in the superheater. In the end, the superheater outlet steam enthalpy tends to be stable about 400 s later than the step change.

4.3. Step Increase of Feed Water Flow

As shown in the model, the feed water flow is also one of the influencing factors of the receiver performance [10]. The designed value of feed water flow in the receiver is 8 t/h. The dynamic responses of characteristic parameters in the cavity receiver are shown in Figures 6 (a)–6 (f) when there is a step increase to 9 t/h, 10 t/h, and 11 t/h of feed water flow.

Figure 6:

The dynamic responses of characteristic parameters with step increase of feed water flow.

As shown in Figure 6 (a), there is a sudden increase of the water-wall outlet dryness that is because the step change of feed water flow can result in a rapid change of pressure in the beginning, and the flash or condensation will appear. And then due to the fact that the inlet enthalpy in the downcomer H _x decreases regardless of the increased feed water flow, the water-wall outlet dryness decreases gradually and reaches the steady state. It follows from (12) that the drum pressure will decrease during the dynamic process, and the superheater outlet pressure decreases more slowly than that of drum pressure, and the main steam flow D _qb is independent of the pressure drop in superheater. Therefore, the main steam flow D _qb increases and tends to be stable about 400 s later than the step change. Figure 6 (e) shows the dynamic response of drum water level. It shows the phenomenon of false water level in the case of a sudden increase in feed water flow. For one thing, the steam cubage in water will decrease due to the supercooling degree of feed water. For another, the length of single-phase section in water wall and the working fluid density will increase, which can result in a decrease of mass storage M _xh in evaporation area. Thus, the above-mentioned result will appear, but the phenomenon of false water level is less serious than that of step change of radiation flux.

The water in the drum will fulfill the drum at 2615 s, 1390 s, and 967 s when there is a step increase to 9 t/h, 10 t/h, and 11 t/h of feed water flow.

Figure 6 (f) shows the dynamic response of superheater outlet steam enthalpy in the receiver. In the dynamic process, the solar energy received in the superheater is essentially constant. Therefore, the main cause of superheater outlet steam enthalpy change is the superheater steam flow D _qb as shown in Figure 6 (d). The superheater outlet steam enthalpy increases gradually and stabilizes to a certain value about 400 s later.

4.4. Step Decrease of Feed Water Flow

The dynamic responses of characteristic parameters in the cavity receiver are shown in Figures 7 (a)–7 (f) when there is a step decrease to 7 t/h, 6 t/h, and 5 t/h of feed water flow.

Figure 7:

The dynamic responses of characteristic parameters with step decrease feed water flow.

As shown in Figures 7 (a)–7 (f), there is a sudden decrease of the water-wall outlet dryness in the beginning, and then the water-wall outlet dryness increases gradually and reaches the steady state. The drum pressure and the superheater outlet pressure will increase during the dynamic process, and the main steam flow D _qb is independent of the pressure drop in superheater. In the end, the main steam flow D _qb increases and tends to be stable about 400 s later than the step change.

Figure 7 (e) shows the dynamic response of drum water level. It shows the phenomenon of false water level. And the water in the drum will dry up at 2835 s, 1441 s, and 992 s when there is a step decrease to 7 t/h, 6 t/h, and 5 t/h of feed water flow.

The dynamic response of superheater outlet steam enthalpy is shown in Figure 7 (f). The superheater outlet steam enthalpy decreases and stabilizes gradually to a certain value owing to the increase of D _qb shown in Figure 7 (d).

5. Conclusions

Based on noncontinuous step change of radiation flux, a nonlinear dynamic model, which gives a comprehensive consideration of flash and condensation in two-phase flow, has been constructed to obtain the effects of the noncontinuous step change radiation flux and step change feed water flow on the receiver performance by sequential modular approach. The study of the thermal dynamic characteristics of the cavity receiver of 1 MW solar power station constructed in Beijing was conducted with a step change radiation flux and feed water flow in this paper. The variation trends of water-wall outlet dryness, drum pressure, main steam flow, superheater outlet pressure, drum water level, and superheater outlet steam enthalpy, were obtained and discussed. We can find that the water-wall outlet dryness, drum pressure, main steam flow, superheater outlet pressure, and superheater outlet steam enthalpy have self-balance ability, and they can tend to be stable in the end. However, the drum water level is easily going to destabilize, thus, necessary measures must be taken to make water-steam system stable. The results obtained could provide general guidance for solar thermal power tower system designing and operation.