Prel. Design Method ORC Centrif. Turbines - ASME ORC2013 155.pdf · Preliminary Design Method For...

Preliminary Design MethodFor Small ScaleCentrifugal ORC TurbinesASME-ORC 2013, 2nd Int. Seminar on ORC Power SystemsRotterdam, 7-8 October

E. Casati1,2, S. Vitale1,M. Pini2,G. Persico2, & P. Colonna11Aerospace Dept., Delft University of Technology2 Energy Dept., Politecnico di Milano

E. Casati , S. Vitale , M. Pini , G. Persico , & P. ColonnaPrel. Design Method µORC Centrif. Turbines 1 / 21

Outline

1 0. Introduction

2 1. ORC Turbine

3 2. The zTurbo code

4 3. Preliminary design of a 10 kWel ROT


IntroductionORC systems ⇒ important for decentralized powergeneration.

- Future development of micro-ORC turbogenerator (10-100kWel)

- WHR from truck engines, concentrated solar, domesticCHP, ...

The turbine represents the most critical component interms of efficiency, compactness, cost.


Outline

1 0. Introduction

2 1. ORC Turbine




ORC Turbine (1/2)

Use of ORC fluids:simple layout, compact and reliable turbine Nstg ↓, U ↓

complex aerodynamic design M ↑ ,(

Vout/Vin

)↑

Large compressibility effect → No similarity rules (Ds, ωs)

=⇒ non-conventional turbine architectures=⇒ reliable preliminary design 1D tool for ORC turbines


ORC Turbine (2/2)

Centrifugal Architecture- D ↑ ⇒ Aflow ↑- “Easy” and compact multi-stage solutions- centrifugal term!!

Leu =V 2

1 −V 22

2 +W 2

2 −W 21

2 +U2

1−U22

2

ORC application Macchi (1977); Casci (1979):- stator-rotor solution, not counter-rotating

(1 generator)

3

2

1

STATORand CASE

(THRUST BALANCING)

ROTOR

VAPOR INLET

VAPOR INLET

VAPOR OUTLET

2

1

3


Outline

1 0. Introduction

2 1. ORC Turbine




zTurbo

zTurbo: 1D design-analysis code (fortran 90)

Turbine preliminary design:

I selecting basic design parameters ⇒ necessary conditionfor a good turbine Macchi (1977, 1985)

I “rigorous” approach ⇒ multi-variable optimization

Main features:

I proper treatment of real gases (LUT)

I multiple turbine architectures

I different loss models


Code Validation (1/3)zTurbo vs test-case TG 4 stages Fottner (1990)

n0 7500 rpmmflow 7.8 kg/sTt,in 413 Kpt,in 2.6 barpout 1.022 barβstg 1.255ris 0.5

Operative conditions

Cross section test-case

αout [◦] S/bax cl/bax bax [mm] tip [mm] Dout/Din

Stator 68 0.81 0.15 49.4 0 1.01Rotor 69.1 1.07 0.6 36.9 0.4 1.01


Code Validation (2/3)

Measured data and zTurbo resultes:

1st 2st 3st 4st

pt [bar]Data (meas.) 2.11 1.68 1.335 1.046zTurbo 2.1 1.66 1.32 1.04err. [%] 0.47 1.19 1.12 0.57Tt [K ]Data (meas.) 386.2 363.1 340.1 320.2zTurbo 391.1 366.0 343.2 323.1err. [%] 1.28 0.82 0.87 0.62Vout [m/s]Data (meas.) 66.1 66.3 62.5 59.5zTurbo 65.48 65.47 61.62 58.55err. [%] 0.93 1.25 1.408 1.59hbld [m]Data 67.5 77.5 89.2 103zTurbo 65.7 75 88.5 0,104err. [%] 2,67 3,23 0,78 0,97

Data zTurbo err. [%]

ηts 0.913 0.894 2.08

- the overall relative error is within theranges of uncertainty of all thestatistics correlations used.

- 3-D turbine⇒ 1-D tool

⇒ reliable procedure.


Code Validation (3/3)

Overlap of real and resulted meridional channel.


Optimization (1/2)

zTurbo doesn’t solve an optimization problem

η = f (ψ,ris, βstg, bax,(

Sbax

), αgeo, ...)


Optimization (1/2)zTurbo + optimization tool.


Optimization (2/2)

zTurbo coupled to an external optimization software Sandia

National Laboratories (2012)

Flexibility:1 objective function(s)2 independent variables3 constraints4 search algorithms

⇒ different optimization strategies


Outline

1 0. Introduction

2 1. ORC Turbine




Thermodynamic cycle

Application ⇒ waste heat recovery from a Diesel engine.

- thermodynamic cycle (input) fromliterature Lang et al. (2013)

- Requirements: efficiency andcompactness

⇒ choice: centrifugal transonicmulti-stage turbine

Parameter Unit Value

Fluid - D4mflow kg/s 0.266Tt,in

◦C 242.5pt,in bar 4.4pout bar 0.087∆hturb,is kJ/kg 48.120βtot - 50.57Vout/Vin - 53


Design strategy (1/3)

First approach ⇒ “repeating-stage” procedure Coomes et al. (1986);

Cerri et al. (2003); Pini et al. (2013)

* independent variables:1 Radial chord⇒ brad,s = brad,r2 Outlet geometric angle⇒ αgeo = −βgeo3 Reaction degree⇒ ris

* Constraint: δ ≤ 30◦

* Objective function: ηφ (φ = 0.5)

R[m]

0

0.1

0.2

0.3

0.4

0.5

statorrotor


Design Strategy (2/3)

Assessing “repeating-stages” in the context of microturbines.

C.E . =Din

Din + brad(1)

hbld, out ∝1

cosβgeoDout(2)

high flaring angle

converging-trend

statorrotor

rδ

⇒ the assumption of the repeating-stages can not be extended to micro-ROTFirst stages ⇒ brad ↓ αgeo, βgeo ↑Last stages ⇒ brad ↑ αgeo, βgeo ↓


Design Strategy (2/3)

Assessing “repeating-stages” in the context of microturbines.

C.E . =Din

Din + brad(1)

hbld, out ∝1

cosβgeoDout(2)

row

1 2 3 4 5 6 7 8 9 10 11 120.6

0.7

0.8

0.9

1

1.1

D/D

inout

⇒ the assumption of the repeating-stages can not be extended to micro-ROTFirst stages ⇒ brad ↓ αgeo, βgeo ↑Last stages ⇒ brad ↑ αgeo, βgeo ↓


Design strategy (3/3)Novel procedure for micro ROT’s

* Independent variables:I brad for each stage (x 5)I αgeo for each blade row (x 10)I Din and nI hbld,in

* Fixed parameters:

geometric parameter value

tcl [mm] 0.1te [mm] 0.1cl/brad [-] 0.1

* Assumptions for transonic machine(M < 1.1):

1 Nstg= 52 βstg= N√βtot3 ris= 0.4

* Constraints:

constraint value

Flaring angle[◦] δ ≤ +7.0

outlet section [mm] o ≥ 1.0aspect-ratio [-] hbld/brad ≥ 0.30

* Objective function: ηφ (φ = 0.5)

* Optimization parameters:

Keyword choice

population size 100mutation type replace uniformconvergence type best fitness trackerpercent change 0.10number of generations 200


5-stages turbine

Optimization results.

Main parameters value

P [kW] 11.19ηφ [-] 0.835n [rpm] 12400Din [m] 0.053Dout [m] 0.18hin [m] 0.002δmax

[◦] 7.00Mmax [-] 1.02(hbld/bout)max [-] 1.84

R[m]

0

0.02

0.04

0.06

0.08

0.1

statorrotor


5-stages turbine





R[m]

0

0.02

0.04

0.06

0.08

0.1

statorrotor

R[m]

0

0.1

0.2

0.3

0.4

0.5


5-stages turbine





stator

rotor

MV2= 0.96

= 0.61MV3

= 0.56

= 0.37

MW3= 0.92

= 0.40

MV = 0.95

MV = 0.98

MV = 1.012

= 0.92

= 0.72

= 0.54

= 0.43

MV = 1.02

= 1.00

= 0.81

= 0.61

= 0.45

= 0.96

MW3= 0.97

MW3= 1.00

MW3= 1.00

MV3= 0.45

MV3= 0.35

MV3= 0.49

MV3= 0.61

MW2= 0.39

= 0.38

= 0.54

= 0.63

1stg

5stg

4stg

3stg

2stg

2

2

2

MU2

MU2

MU2

MU2

MU2

MW2

MW2

MW2

MW2

MW3

M3U

M3U

M3U

M3U

M3U


SummaryComparing the 3 machines...

Results 5-stages 4-stages 3-stages

P [kW] 11.19 10.9 10.51ηφ [-] 0.835 0.818 0.799ηts [-] 0.823 0.802 0.773∆η [%] 1.43 1.95 3.25Mmax [-] 1.02 1.2 1.33n [rpm] 12400 14300 15400Din [m] 0.053 0.048 0.057Dout [m] 0.18 0.169 0.162hin [m] 0.002 0.0023 0.0021δmax

[◦] 7.05 7.15 11.75hout [m] 0.0146 0.0131 0.0182(hbld/bout)max [-] 1.84 1.67 1.38

R[m]

0

0.02

0.04

0.06

0.08

0.1

number of stages

3 4 5

statorrotor

Dout =1

πhbld,out

(Vout

Vin

)(Vrad,inAin

Vrad,out

)(3)


ROTs vs RIT

Comparison with a radial-inflow single-stage turbine.

1 higher efficiency

2 similar dimension

3 half rotational speed

4 lower disk friction losses (∼ 15 )

Ploss,df = ωcmρD3outU

2out (4)

5-st 4-st 3-st 1-st (RIT)

P [kW] 11.19 10.9 10.51 10.3ηis [-] 0.835 0.818 0.799 0.78 (?)Mmax [-] 1.02 1.2 1.33 N.A.n [rpm] 12400 14300 15400 26000Dout [m] 0.18 0.169 0.162 0.16

5-st 4-st 3-st 1-st (RIT)

Ploss,df [W] 37.36 41.80 42.26 191.32Ploss,df/P [%] 0.33 0.38 0.40 1.86Ploss,df/Ploss,RIT [%] 19.0 21.8 22.1 -


Conclusions

zTurbo + optimizer ⇒ reliable and flexible design tool

Novel design strategy for micro centrifugal turbinespresented

centrifugal architecture promising for (micro)ORC systems


THANK YOU FOR YOUR ATTENTION


ReferencesCasci, C. (1979). Macchine a fluido bifase (in Italian). Tamburin.

Cerri, G., Battisti, L., & Soraperra, G. (2003). Non conventional turbines for hydrogenfueled power plants. In Proceedings of the ASME Turbo Expo 2003 GT2003-38324.Atlanta, GA.

Coomes, E., Dodge, R., Wilson, D., & McCabe, S. (1986). Design of ahigh-power-density Ljungstrom turbine using potassium as a working fluid. SanDiego, CA, USA,: Intersociety energy conversion engineering.

Fottner, L. (1990). Test cases for computation of internal flows in aero enginecomponents. AGARD, .

Lang, W., Almbauer, R., & Colonna, P. (2013). Assessment of waste heat recovery fora heavy-duty truck engine using an ORC turbogenerator. Journal of Engineering forGas Turbines and Power-Transactions of the ASME , 135, 042313–1–10.

Macchi, E. (1977). Lecture series 100 on closed-cycle gas turbines. chapter Designcriteria for turbines operating with fluids having a low speed of sound. Von KarmanInstitute for Fluid Dynamics.

Macchi, E. (1985). Design limits: Basic parameter selection and optimization methodsin turbomachinery design. (pp. 805–828). Izmir, Turk: Martinus Nijhoff Publ,Dordrecht, Neth volume 97 A v 2.

Pini, M., Persico, G., Casati, E., & Dossena, V. (2013). Preliminary design of acentrifugal turbine for organic Rankine cycle applications. Journal of Engineering forGas Turbines and Power-Transactions of the ASME , 135, 042312–1–9.


References (cont.)

Sandia National Laboratories (2012). The Dakota project - Large Scale EngineeringOptimization and Uncertainty Analysis. Http://dakota.sandia.gov/software.html (lastaccessed September 2013).


Prel. Design Method ORC Centrif. Turbines - ASME ORC2013 155.pdf · Preliminary Design Method For...

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