Solar receiver modeling: Linear receivers - SOLLAB SUMMER... · Collector (PTC) Linear Fresnel...

María Isabel Roldán, PhD e-mail: [email protected]

Juan José Serrano, PhD Student e-mail: [email protected]

Solar receiver modeling: Linear receivers

Summer School June 2014


1. Basic terms & concepts 2. Simulation (Introduction) 3. 1-D Modelling (steady state) 4. 2-D Modelling (steady state) 5. 3-D Modelling (steady state) 6. CFD modelling 7. Summary

Contents


1. Basic terms & concepts

1.1 Linear Solar Receivers (PTC vs LFC)

1.2 PTC general overview

1.3 Basic concepts in PTC simulation

1. Simulation Methods


5


Parabolic Trough Collector (PTC)

Linear Fresnel Collector (LFC)


6


Advantages Disadvantages

• Higher overall efficiency.

• Commercially extended.

• More mature technology.

• Higher optical efficiency.

• Better distributed production during the day.

• More expensive than Fresnel (Reflector array-tracking, Ball joints, etc… ).

PTCs


7


Advantages Disadvantages

• Better wind resistance.

• Reduced gaps between adjacent rows.

• Reaches higher operation pressure (DSG) , no movable joints required.

• Significant cost reduction potential .

• Lower optical efficiency (secondary reflector).

• Peak production around solar noon.

Fresnel

(G. Morin et al, 2011)


8


Daily generation dist.

(G. Morin et al, 2011)


9


Main components:

Structure

Foundations

Brackets

Single-axis tracking

Thermal Insulation


10


Main components:

Reflectors

HCE

The aperture plane is perpendicular to the one containing the Sun vector


11


Main components (HCE):

Steel absorber

Glass Envelope

Vacuum annulus

Glass-to-metal seal


12


Modified from (A.A. Hachicha et al, 2013) Exp. sunshape from (A. Neumann et al, 2002)

Incoming rays-Optical Model


13


(M.I. Roldán et al, 2013)

Incoming rays-Optical Model


14


(R. Vasquez-Padilla et al, 2011)

Heat transfer-Thermal Model


2. Simulation (Introduction)

2.1 Introduction

2.2 Experimental Facility

2. Simulation (Introduction)


16

2.1 Introduction

Experimental evaluation

Test-facility construction

Economic and time costs

Process simulation

Analysis of several configurations and operating conditions without

economic cost

Theoretical evaluation

High-level programming

languages MATLAB

Computational Fluid Dynamics

(CFD)

FLUENT, COMSOL,

STAR-CCM+…


17

2.1 Introduction

Substantial reduction of lead times and costs of new designs.

Ability to study systems where controlled experiments are difficult or impossible to perform.

Ability to study systems under extreme conditions.

Large volumes of results to obtain a detailed description of the domain analyzed.

Simulation advantages:

Simulation disadvantages:

χ Assumptions to reduce the model complexity to a manageable level.

χ Inability to prove conclusively the convergence of a numerical solution scheme.

χ Convergence does not ensure the obtaining of good results Validation


18

2.2 Experimental Facility

(H. Lobón et al, 2014)

DISS facility scheme at PSA

Operation modes: Recirculation mode

One-through mode

Injection mode


3. 1-D Modelling (steady state)

3.1 Domain definition

3.2 Heat transfer mechanisms

3.3 Numerical solution

3. 1-D modelling


20

3.1 Domain definition

(R.V. Padilla et al, 2011)


21


(R.V. Padilla et al, 2011)

Abbreviations: • f: fluid • a: absorber • e: envelope • s: sky • sa: surrounding air • abs: absorbed • i: node i

Steel absorber Glass envelope


22


Absorber-Fluid forced convection

2

, ,2

f p f a f conv

Vm C Q

z

, f f a fa f convQ Nu k T T

0.11

1

2/32

(C / 2) Re 1000 Pr Pr

Pr1 12.7(C / 2) Pr 1

f D

f

wf

Nu


23


Heat transfer from absorber to envelope

,conv ,conv

,rad ,

aa a a f a e

a e cond bracket a abs

TA k Q Q

z z

Q Q Q


24



,conv ,conv ,rad ,a

a a a f a e a e cond bracket a abs

TA k Q Q Q Q Q

z z

10c

KnL

At very low pressures:

,,conv a e o a a ea eQ h D T T

,

, , , ,ln / / 12

g

a eo a

i e o a i e o a

kh

DD D b D D

202.331 10a e

air

T

P

Free molecular regime


25



,conv ,conv ,rad ,a


TA k Q Q Q Q Q

z z

4 4

,

,conv,

,

, , i,e

11

o a a e

a eo a

i e

o a i e

D T TQ

D

D

Assumptions:

Gray surfaces

Diffuse reflections

Long cylinders

Isothermal cylinders

Opaque envelope to infrared rad.


26



,conv ,conv ,rad ,a


TA k Q Q Q Q Q

z z

(R. Forristal, Tech. report, 2003)


27



,conv ,conv ,rad ,a


TA k Q Q Q Q Q

z z

,

b b b CS base amb

cond bracket

HCE

h P k A T TQ

L

Abbreviations: • Pb: Perimeter of the bracket • Acs: Cross-sectional area bracket • kb: conduction coeff. • LHCE: HCE length • Tbase: temperature at base of bracket • Tamb: ambient temperature • hb: external flow convection coeff. (Churchill & Chu)


28



,conv ,conv ,rad ,a


TA k Q Q Q Q Q

z z

shadow tracking geom reflec dirt envelope dirt

( ) Iclean e a bna absQ K

Nomenclature: • 𝝆𝒄𝒍𝒆𝒂𝒏: Clean mirror reflectivity • 𝜸: intercept factor • 𝝉𝒆: envelope transmittance • 𝜶𝒂: absorber absorptance • 𝑲(𝜽): incident angle modifier • Ibn: Incoming rad at node n


29



,conv ,conv ,rad ,a


TA k Q Q Q Q Q

z z

MC Ray-Tracing

(J.J. Serrano-Aguilera et al, under review)


30


Heat transfer from envelope to the ambient

,conv ,rad ,conv ,rade

e e a e a e e sa e s e abs

TA k Q Q Q Q Q

z z


31





TA k Q Q Q Q Q

z z

,e,conv e o ee saQ h D T T

,

e ee

o e

Nu kh

D

¿Natural or Forced convection?

No wind case: Churchill & Chi correlation

Wind case: Zhukauskas correlation


32





TA k Q Q Q Q Q

z z

4 4

, ,,conv o e o e e skye sQ D T T

Assumptions:

Envelope: small convex gray surfaces

Sky: large blackbody cavity

No exchange with reflector considered

8sky ambT T K


33





TA k Q Q Q Q Q

z z

( ) Iclean e bne absQ K


34


High-level programming languages: Matlab, Python, EES, etc.

Steps to follow:

Discretization of the PDE System

Non-Linear algebraic system

BC

Algebraic system solver algorithm

Algorithm programming


35


Object-oriented modeling languages: Modelica

(J. Bonilla et al, 2012)



4.1 Domain definition & discretization

4.2 Heat transfer mechanisms (HTF-Absorber)

4. 2-D modelling (steady state)


37


Axial & azimuthal discretization

(A.A. Hachicha et al, 2013)


38

4.2 Heat transfer mechanisms (HTF-Absorber)

Axial & azimuthal discretization

Abbreviations: • hconv: Convective heat transfer coeff. • N𝜽: Number of nodes in the azimuthal coord. • Ta

ij : Absorber temperature • Tf

i : HTF temperature

,

ij ij i

a f conv f f a fq Nu k T TN

,

ij

a f convq , ,

1

Ni ij

a f conv a f conv

j

Q q

,

i

a f convQ

i

fh

1i

fh




5. 3-D modelling


40


3D discretization

(J.J. Serrano-Aguilera et al, under review)


6. CFD modelling

6. CFD modelling

6.1 Introduction

6.2 CFD vs Thermal Models

6.3 CFD simulation procedure

6.4 Governing Equations

6.5 Simulation of the DISS facility

6.6 Results & conclusions


42

6.1 Introduction

¿ Why CFD?

Non Linear terms

Arbitrary BC

Variable properties

Multiphysics simulation


43

6.2 CFD vs Thermal Models

CFD:

Fluid dynamics Eq.

Buoyancy forces

Computational cost

Easy programming (GUI)

Black box programming

Thermal Models:

Convection Correlations

Constant Temp. Correlations

Lighter problem

Hard code programming

Customized model


44

6.3 CFD simulation procedure

Pre-processing

Solving

1. Geometry definition 2. Mesh generation 3. Selection of physical and chemical phenomena 4. Definition of fluid properties 5. Specification of appropriate boundary conditions

1. Approximation of the unknown flow variables by simple functions 2. Discretization by substitution of the approximations into the governing flow equations and subsequent mathematical manipulations 3. Solution of the algebraic equations

Finite Volume Method

Post-processing Data visualization tools: domain geometry and grid display, vector plots, line and shaded contour plots, 2D and 3D surface plots, particle tracking, view manipulation, color postscripts output…

OPTIMIZATION/NEW DESIGNS

CFD SIMULATION: PROCEDURE


45

6.4 Governing equations

Continuity equation

𝝏𝝆

𝝏𝒕+ 𝜵 𝝆 ∙ 𝒗 = 𝑺𝒎 Density

Momentum equation

𝝏

𝝏𝒕𝝆 ∙ 𝒗 + 𝜵 𝝆 ∙ 𝒗 ∙ 𝒗 = −𝜵𝒑 + 𝜵 ∙ 𝝉 + 𝝆 ∙ 𝒈 + 𝑭

Energy equation

𝝏

𝝏𝒕𝝆 ∙ 𝑬 + 𝜵 · 𝒗(𝝆 ∙ 𝑬 + 𝒑) = 𝜵 · 𝒌𝒆𝒇𝒇𝛁𝑻 − 𝒉𝒋 · 𝑱𝒋 + 𝝉𝒆𝒇𝒇 · 𝒗

𝒋

+ 𝑺𝒉

Elapsed time

Velocity vector Mass source

Pressure

Stress tensor

Gravitational body force

External body forces

Energy transfer Effective conductivity

Temperature

Enthalpy of species j

Diffusion flux of species j

Viscous stress tensor

Volumetric heat source


46

6.4 Governing equations

Surface boiling heat flux (Rohsenow correlation)

𝒒𝒃𝒘 = 𝝁𝒍 · 𝒉𝒍𝒂𝒕𝒈 · 𝝆𝒍 − 𝝆𝒗𝝈

·𝒄𝒑𝒍 · 𝑻𝒘 − 𝑻𝒔𝒂𝒕

𝑪𝒒𝒘 · 𝒉𝒍𝒂𝒕 · 𝑷𝒓𝒍𝒏𝒑

𝟑.𝟎𝟑

Liquid viscosity

Latent heat

Liquid density

Vapor density Liquid specific heat capacity

Liquid/surface-combination constant

Wall temperature

Saturation temperature

Liquid Prandtl number and exponent

Surface tension


47


Domain selection: Facility

Selection of operation mode

Definition of interconnections between solar collectors

Independent simulation of each collector, using output variables as input parameters in the next collector, in order to minimize computational requirements

Simulation of the absorber-tube geometry. The influence of the surrounding area is considered in the boundary conditions.



48


Domain selection: Collector

Definition of the section in the collector loop (preheating, boiling or superheating)

Subdomains:


Fluid

Absorber tube (irradiated/non irradiated sections)



49


Absorber section


Fluid

Mesh definition (CFD simulation)

Internal fluid region: Flow aligned hexahedral cells

Near wall flow region: Well-adapted prismatic cells

Solid region: Well-adapted prismatic cells

Mesh size: Good compromise between reasonable grid-independence of the solution and computational cost


50


General assumptions

Optical, geometrical and thermal losses included as boundary condition in the absorber-tube domain

Source: Plataforma Solar de Almería

Horizontal absorber position

Forced fluid flow

Neglected gravitational force

Uniform relative roughness of the pipe

Transient and turbulent flow regimes (k-ε model/RNG model)

Tracking errors no considered


51


Measurement uncertainties influence the boundary conditions of each simulation (effective heat flux, mass flow, inlet fluid temperature…)

Evaluation

Selection of the uncertainty range for each variable used as boundary condition

Definition of the variable with greater influence on simulation results

Substitution of the variable value by both limits of its uncertainty range (two different calculations)

Simulation results allow defining an error bar for each measurement point by the comparison with the numerical data obtained from the original boundary conditions


52

6.6 Results & conclusions

Validation

Fluid pressure gradient

Thermal gradient in the absorber pipe/fluid

Volume fraction vapor (L. Valenzuela, 2012) Temperature, K

Temperature, K

Fluid

Absorber pipe

(M.I. Roldán et al, 2013) (D. H. Lobón, 2014) (D. H. Lobón, 2014) (D. H. Lobón, 2014)

Fluid velocity


53

7. Summary

Simulation and theoretical evaluation allow to analyze more

diverse cases and configurations reducing costs and time respect

to the experimental approach.

Thermal models based on experimental heat transfer correlations

lead to faster simulations (lower computational load).

CFD simulations provide a detailed description of heat transfer

mechanisms without requiring experimental information.

Validation is always required.


Thank you for your

attention

María Isabel Roldán, PhD e-mail: [email protected]

Juan José Serrano, PhD Student e-mail: [email protected]

Date post:	18-Mar-2018
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Solar receiver modeling: Linear receivers - SOLLAB SUMMER... · Collector (PTC) Linear Fresnel...

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