Geometric Design of Micro Scale Volumetric Receiver Using System-Level Inputs An Application of Surrogate-Based Approach

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Geometric Design of Micro Scale Volumetric Receiver

Using System-Level Inputs: An Application of

Surrogate-Based Approach

Tufan Akbaa,b,∗, Derek K. Bakerc,d, M. Pınar Meng¨u¸ca,b

aDepartment of Mechanical Engineering, Ozyegin University, Istanbul, Turkey

bCenter for Energy, Environment and Economy (CEEE), Ozyegin

University, Istanbul, Turkey

cDepartment of Mechanical Engineering, Middle East Technical

University, Ankara, Turkey

dCenter for Solar Energy Research and Application (GUNAM), Middle East Technical

University, Ankara, Turkey

Abstract

Concentrating solar thermal power is an emerging renewable technology with

accessible storage options to generate electricity when required. Central re-

ceiver systems or solar towers have the highest commercial potential in large-

scale power plants because of reaching the highest temperature. With the

increasing solar chemistry applications and new solar thermal power plants,

various receiver designs require in micro or macro-scale, in materials, and

temperature limits. The purpose of the article is computing the geometry of

the receiver in various conditions and provide information during the concep-

tual design. This paper proposes a surrogate-based design optimization for

a micro-scale volumetric receiver model in the literature. The study includes

creating training data using the Latin Hypercube method, training ﬁve dif-

ferent surrogate models, surrogate model validation, selection procedure, and

surrogate-based design optimization. Selected surrogates have over 98% R2

ﬁt and less than 4% root mean square error. In ﬁnal step, optimization per-

formance compared with the base model. Because of the model complexity,

surrogate models reached better objective values in a signiﬁcantly shorter

time.

∗Corresponding author.

Email address: tufan.akba@ozu.edu.tr (Tufan Akba)

Preprint submitted to - October 18, 2022

arXiv:2210.09249v1 [physics.flu-dyn] 17 Oct 2022

Keywords: surrogate modeling, concentrating solar thermal, receiver,

OpenMDAO, optimization

List of Symbols

cpspeciﬁc heat at constant pressure [J/kg ·K]

hheat transfer coeﬃcient [W/m2·K]

kthermal conductivity [W/m ·K]

q00 heat ﬂux [W/m2]

rinner radius [m]

Llength [m]

sspeciﬁc surface [m−1]

Ttemperature [K]

vvolume [m3]

ρdensity [kg/m3]

Subscripts

fﬂuid

ssolid

rradiation

Acronyms

CST concentrating solar thermal

DOE design of experiments

HCE heat collecting elements

HTF heat transfer ﬂuid

LHD Latin hypercube design

MDO multidisciplinary design optimization

RBF radial basis function

RMSE root mean square error

SLSQP sequential least squares programming

TES thermal energy storage

1. Introduction

Thermodynamic cycle analysis gives insight into the overall system per-

formance and shows irreversibilities in each process creating the system [1].

For a system design (i.e. power plant, gas turbine, internal combustion en-

gine), thermodynamic cycle analysis is the top-level model and deﬁnes the

expected performance of the components as the initial phase. After the

component design is completed, the cycle analysis is performed with the new

values to observe the system-level impact for providing feedback information.

Thermodynamic cycle analysis is the core calculation for systems in diﬀerent

performance parameters, design limitations, and operation conditions. Fossil

to renewable transition changed the analysis structure and performance pa-

rameters, design limitations, and operation conditions. The known method

from the fossil-fueled systems, fuel is the controlled input for optimization of

the plant eﬃciency by adjusting the fuel [2, 3, 4]. Unlike fossil fuels, renew-

able energy sources are not controlled inputs. The thermodynamic models

focus on maximizing cumulative power generation by creating multiple op-

eration points instead of optimizing the most eﬃcient conﬁguration [5, 6].

For concentrating solar thermal (CST) power, solar ﬁeld, auxiliary heater,

thermal energy storage (TES), and power block are the main components of

the plant. The possible combinations of these components deﬁne the mul-

tiple operation points of the thermodynamic analysis [7]. Deﬁning design

requirements gets more complex in multiple operation points. System-level

simulations are required for veriﬁcation of the component design at multi-

ple points. The current study focuses on component design integration in

the thermodynamic cycle analysis. The coupled design (thermodynamic sys-

tem performance and integrated component design) will solve the problem

and satisfy these requirements together. However, coupled modeling requires

multidisciplinary design optimization (MDO) and requires a problem archi-

tecture rather than solving every step separately [8].

The need for MDO arose to solve multiple subproblems in diﬀerent dis-

ciplines for complex engineering systems. MDO helps to solve these systems

in two ways. The ﬁrst is coupling the system with all the interdisciplinary

interactions. The second way is optimizing all the design variables coupled,

and the trade-oﬀs of the subproblem design considerations [9]. The optimiza-

tion problem may diverge because of the computational load while solving

the subproblems simultaneously or due to the structure of the optimization

problem. One alternative to converge the optimization problem is using

an approximate (called surrogate) model that retains suﬃcient accuracy to

represent model complexity in an error range. Surrogate modeling has ad-

vantages for gradient-based optimization, especially when the model has a

high variation of gradients (i.e. noisy data) [10].

Surrogate models or metamodels are used for simplifying complex en-

gineering models. These models are less accurate but can provide a fast

alternative to original models. The accuracy of the model is estimated be-

fore using the model. A surrogate model is evaluated by its computational

time and accuracy [11]. Several surrogate models can be found in the lit-

erature. Response surface methodology [12] is one the fastest method for

surrogate modeling and kriging [13] is the most common alternative origi-

nating from mining applications. Because of the computational load of the

kriging, ﬁrst or second order response surfaces created to observe the surro-

gate performance and accuracy of the surrogate model increases using kriging

in most of the cases. Neural networks are another surrogate model method

that provides solution alternatives in the form of chains of simple functions.

These chains are called networks, and each calculation node is called a neu-

ron [14]. The accuracy of the surrogate model is highly dependent on the

sample or training data. The term ”design of experiments (DOE)” focuses

on reﬂecting the model behavior by screening the required number of samples

called experiments [15]. There are several sampling methods like Latin hy-

percube design (LHD), factorial designs, random selection, orthogonal arrays

and low-discrepancy sequences [16, 17, 11, 10] for training accurate surrogate

models.

One advantage of surrogate modeling is the eﬃcient solution of multiﬁ-

delity problems. It maintains the required model complexity in the design

phase, and the surrogate model transfers the required information for sys-

tem optimization. The eﬀectiveness of this approach was observed in several

studies in diﬀerent designs such as battery thermal management system [18],

permanent magnet synchronous motor [19], battery package optimization

[20]. A similar approach is the core idea explained in the article. The ac-

tual model is used for an accurate solution. Training data is generated using

the model for surrogate training and optimization is performed using the

surrogate model.

The current study explains an integrated way of receiver modeling. Re-

ceivers are the solar radiation collecting elements in CST power plants. Sev-

eral receiver models are existing in the literature [21, 22, 23] and ETH’s

receiver model [24] is replicated in this study. The main purpose of the ar-

ticle is to ﬁll the gap in component design in CST technology, especially

in multiple operating conditions, and represent the results for proving that

surrogate modeling is an eﬃcient way of ﬁnding the optimum solution in com-

plex design problems. In the article, diﬀerent surrogate models are trained

and their performances are compared with the base model (replicated model

used cases) for validation purposes. After valid surrogates are selected, op-

timizations are performed with the selected surrogate model and the base

model. Optimization results and the ﬁnal optimum points are compared as

the output of the study. The content of the article is structured as follows:

In section 2, governing equations of the replicated receiver model and prob-

lem statement are explained. Section 3 focuses on building the surrogate

model and optimization. Performance metrics, other ﬁndings, results, and

discussion are in Section 4. The ﬁnal remarks and conclusion are in Section

2. Problem Statement and Numerical Model

Receivers have three distinct designs: In external receivers, liquid heat

transfer ﬂuid (HTF) passes through the heat collecting elements (HCE) which

are exposed to concentrated solar radiation. In solar tower (or central receiver

system), external receivers are widely used in large-scale power generation

from Solar One, the pilot central receivers system in the late 1970s, to re-

cent state-of-the-art large-scale plants including Gemasolar, Crescent Dunes,

Noor3, Delingha, and others [25]. Internal receivers are enclosed, and solar

radiation is concentrated in an opening. These receivers are selected in solar

tower power plants if the reﬂector ﬁeld is directional. HCE are enclosed for

decreasing the ambient losses [26].

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GeometricDesignofMicroScaleVolumetricReceiverUsingSystem-LevelInputs:AnApplicationofSurrogate-BasedApproachTufanAkbaa,b,,DerekK.Bakerc,d,M.PnarMenguca,baDepartmentofMechanicalEngineering,OzyeginUniversity,Istanbul,TurkeybCenterforEnergy,EnvironmentandEconomy(CEEE),OzyeginUniversity,Istanbul,Turk...

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Geometric Design of Micro Scale Volumetric Receiver Using System-Level Inputs An Application of Surrogate-Based Approach

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