Numerical and experimental investigation to visualize the fluid flow and thermal characteristics of a cryogenic turboexpander

Energy xxx (xxxx) xxx

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Numerical and experimental investigation to visualize the fluid flow and thermal characteristics of a cryogenic turboexpander Manoj Kumar a, *, Suraj K. Behera a, Amitesh Kumar, [email protected] b, Ranjit K. Sahoo a a b

National Institute of Technology Rourkela, Odisha, 769008, India Indian Institute of Technology, Varanasi, U.P, 221005, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 February 2019 Received in revised form 18 September 2019 Accepted 1 October 2019 Available online xxx

The increasing demand for cryogenic fluids is acquiring the research attention to develop efficient machines to produce cryogenic temperature such as turboexpander based system. The expansion turbine and nozzle of a turboexpander are the critical components of such systems, and its performance has a significant effect on the overall efficiency of the system. In this paper, the effective design methodology of a radial inflow turbine by considering different loss models is presented. The methodology consists of one-dimensional modeling to describe the geometrical parameters of the nozzle and turbine. The optimal range of important non-dimensional variables such as blade speed, pressure ratio, ratio of hub and shroud radius to turbine inlet radius are predicted using artificial intelligence techniques for better performance of the turbine. This approach improves the turbine efficiency and power output by 4% and 18:9% respectively as compared to the existing model. The three-dimensional numerical investigation is carried out to visualize the fluid flow and thermal characteristics of the designed turbine and nozzle. The study also focuses on to identify the flow separation zone, tip leakage flow, vortex formation, secondary losses and its reasons at different spanwise locations of the turbine. Additionally, Sobol sensitivity analysis method is used to distinguish the significance of different assumed constants on the total losses and non-dimensional design variables on total-to-static efficiency. Finally, the numerical results are validated with experimental data of a case study. The study highlights the importance of the design methodology, the prediction capability of artificial intelligence method, Sobol sensitivity analysis, the experimental techniques and benchmarking model for numerical analysis at different cryogenic temperature. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Turboexpander Experimental techniques Artificial intelligence techniques Sobol sensitivity analysis

1. Introduction The usage of cryogenic temperature is essential, for example, to produce an inert environment (shielding gas) in the welding process, leak detectors, optical fibers, solar telescopes, superconductivity and superfluidity, space appliances, biomedical and chemical instruments, etc. [1]. This increases the demand for cryogenic fluids and to fulfill the requirement, it is necessary to develop an efficient reversed Brayton cycle based turboexpander system. High-speed radial inflow turbine (RIT) is the cooling component of these systems. Therefore, the design and development of an efficient turbine

* Corresponding author. NIT Rourkela, Odisha, 769008, India. E-mail addresses: [email protected] (M. Kumar), [email protected] (S.K. Behera).

is necessary. In recent decades, Whitfield et al. [2] and Aungier [3] proposed the preliminary design of a radial inflow turbine. Generally, the efficiency of the small radial turbine is relatively low as compared to large gas turbines. Therefore, researchers are interested in increasing the efficiency of the small turbine by minimizing the losses which may cause the improved performance of the smallscale turboexpander system [4]. Suhrmann et al. [5] developed a correlation for loss models which improves the design methodology of a small-scale radial turbine. The blade profile losses obtain due to boundary layer formation near the surface of the blade. The growth of the boundary layer depends on the aerodynamic profile of the turbine blades which causes the boundary layer separation. It can be reduced either by decreasing the blade thickness at leading and trailing edge [6]. Several techniques (active and passive) were proposed to eliminate these losses for the turbine and compressor

https://doi.org/10.1016/j.energy.2019.116267 0360-5442/© 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

Variables b bt C c Chn Cmt Cqt D Di ðYÞ Dh Dt ds d g h k kxr Lh Lt M m m_ n ns P Pn p Q Rh Rs R2 rp Si

j c l ls Q h

Blade height ðmÞ Nozzle height ðmÞ Absolute velocity ðm =sÞ Turbine blade chord Chord length ðmÞ Nozzle throat velocity (Meridional component) ðmmÞ Nozzle throat velocity (Tangential component) ðmmÞ Rotor diameter ðmÞ First-order derivative Mean passage hydraulic diameter ðmÞ Nozzle throat circle diameter ðmÞ Specific diameter Diameter ðmÞ Activation function Enthalpy ðkJ =kgÞ Discharge coefficient, Hidden neurons (ANN) Cross coupling coefficient Mean passage hydraulic length ðmÞ Total losses Mach number Outputs Mass flow rate ðkg =sÞ Number of input neuron Specific speed Power ðkWÞ Blade pitch length ðmÞ Pressure ðPaÞ Volume flow rate ðm3 =sÞ Hub radius ðmÞ Shroud radius ðmÞ Turbine inlet radius ðmÞ Pressure ratio First-order sensitivity index Density ðkg =m3 Þ Flow coefficient Stage head coefficient Absolute meridional velocity ratio Hub ratio Stagger angle Rotor meridional velocity coefficient Efficiency

Subscripts h is m n r

Hub Isentropic Meridional Nozzle Radial

r

4

[7]. Denton [8] explained that the secondary losses are obtained due to the end wall boundary layer, tip leakage, vortices and boundary layer separation near the suction side. It may exist because of reversed flow due to the adverse pressure gradient. The vortices are generated due to the mixing of secondary flow to the mainstream. It occurs due to aerodynamic losses and a major reason for diminishing the performance of the turbine. Ventura et al. [9] estimated the performance of a radial turbine considering different established loss models: tip clearance, incidence, trailing

s t U VarðYÞ vs W Wt w2mj ; w1ji

Meridional streamlength ðmÞ Blade thicknessðmÞ Blade speed ðm =sÞ Total variance of the output Speed ratio Relative velocity ðm =sÞ Throat widthðmÞ Synaptic weights

X xi Y ym Z Zr

Parameters Value of incoming data Target function Output of the neuron Number of blades Rotor axial length ðmÞ

Acronyms ANFIS ANN GGI MAE ORC PFHX RIT

Adaptive neuro-fuzzy inference system Artificial neural network Generalized grid interface Mean absolute error Organic Rankine cycle Plate-fin heat exchanger Radial inflow turbine

Greek symbols Absolute velocity angle ðdegreeÞ Nozzle throat angle Absolute flow angle ðdegreeÞ Incidence angle ðdegreeÞ Axial clearance ðmÞ εx εr Radial clearance ðmÞ hts Total to static efficiency jz Zweifel number u0 Accentric factor u Rotational speed of turbine ðRPMÞ g Specific heat ratio s Shroud t Throat ts Total-to-static tt Total-to-total x Axial I Incidence loss Cl Clearance loss TEL Trailing edge loss BL Blade loading loss rel Relative 0 Stagnation condition 1 Nozzle inlet 2 Turbine inlet 3 Turbine outlet

a at b b2;opt

edge, passage, exit energy, and windage. Klonowicz et al. [10] discussed the effect of passage and partial admission loss models on the performance of a turbine used in an organic Rankine cycle. The usage of artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) are demanding because of its unique features like, reliable, fast response and computationally less expensive [11]. Ghorbanian and Gholamrezaei [12] revealed the usage of an artificial neural network for prediction of performance characteristics of a compressor. Several researchers reported

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the usage of ANN and ANFIS models to predict the performance of gas turbines. Bartolini et al. [13] applied these methodologies for performance prediction of micro gas turbines. Several experimental studies have conducted to determine the performance of the reversed Brayton cycle-based turboexpanders system. Hongli et al. [14] performed an experimental analysis to investigate the performance of a turboexpander used in reversed Brayton cycle-based air refrigerator. Ghosh et al. [15,16] conducted an analytical and experimental study of a high-speed cryogenic turboexpander. Zhang et al. [17] developed a radial turbine based prototype turboexpander for air separation system. The results show that the prototype has maximum isentropic efficiency ð10:4%Þ at inlet pressure of 1.7 MPa and 3200 rpm. Chen et al. [18] studied the coupling performance of high-speed turboexpander compressor for reversed Brayton cycle refrigerator at ambient temperature. In recent decades, the evolution of computational fluid dynamics explore many aspects like advancement in aerodynamic profile, flow field characteristics and various losses occurred inside different components of a turboexpander. Kang et al. [19] designed a two-stage radial turbine to increase the performance of an ORC. Harinck et al. [20] carried out a three-dimensional numerical investigation for a set of a nozzle, radial turbine, and diffuser used in an ORC cycle. Streit and Razani [21] proposed the thermodynamic optimization of the expander. The cooling power, aerodynamic design, high rotational speed, etc. extract the interest of the researchers for the rapid development of turbine design [22]. A comprehensive literature review demonstrates that there is a limited number of works available to predict the performance of RIT using ANN and ANFIS models. But none of them develop such models for predicting the performance characteristics of a cryogenic turbine. Apart from this, very few experimental and numerical works are available which investigate the flow field and performance of a turboexpander at cryogenic temperature. This paper attempts to clinch this literature gap. The present study deals with an effective and comprehensive one-dimensional design methodology for designing an RIT considering different loss models. Sobol sensitivity analysis is carried out to identify the effect of major non-dimensional design variables and different constants on total-to-static efficiency and total losses respectively. The optimal range of non-dimensional design variables is predicted by developing an artificial intelligence model for better performance of RIT. Based on the predicted ranges, two turbine and nozzle models are developed. The obtained turbine dimensions are further validated with available results in the open literature which show that the present model increases the total-to-static efficiency and power output by 4% and 18:9% respectively. The numerical simulations are carried out to visualize the fluid flow and thermal characteristics of the working fluid inside the turbine and nozzle using ANSYS CFX. The fluid flow

3

properties, such as Mach number, pressure variation, Reynolds number, density and thermal characteristics, such as static enthalpy, static entropy, temperature variation, Prandtl number, etc. are presented at mid-span and along with the streamwise location. A detailed study of the flow field is visualized with velocity vectors which are essential to identify the losses and reasons for its occurrence. Additionally, the experimental test-rig is developed to analyze the performance of turboexpander and validation of numerical results. The results indicated that the proposed design methodology, sensitivity analysis, ANN and ANFIS model, experimental procedure and numerical results could be applied to develop an efficient turboexpander for reversed Brayton cyclebased gas liquefaction cycles. 2. Design procedure of turbine and nozzle 2.1. One-dimensional design of radial inflow turbine The one-dimensional (1-D) design methodology of a radial inflow turbine (RIT) is introduced to save time because of excessive empirical correlations are employed in this process [3]. The thermophysical properties of the working fluid (nitrogen) have a significant effect on the aerodynamic design of the RIT [23]. Generally, the cryogenic fluids are diatomic gas, and its thermophysical

Fig. 1. Flowchart for 1-D design of a radial turbine.

Table 1 Ranges of different parameters of radial turbine design for cryogenic applications. Design variables Inlet stagnation Pressure (bar) Inlet stagnation Temperature (K) m_ (kg/s) Tip clearance (mm) u (RPM) L=D Blade speed ratio Blade inlet angle (Degree) Blade exit angle (Degree) Z

Other reasonable variables 8  10 90  180 0:01  0:09 0.1 80; 000  150; 000 0:35  0:46 0:60  0:82 72  82  2:8  3:6 10  15

Speed ratio ðvs Þ Rs =R2 Rh =R2 rp

0:62  0:70 0:76  0:96 0:22  0:30 2 5

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Fig. 2. Velocity triangles at (a) Inlet (b) Outlet of the rotor.

Fig. 5. Sensitivity analysis of non-dimensional design variables on total-to-static efficiency. Fig. 3. Rotor geometry details.

Fig. 4. Sensitivity analysis of total losses (a) Dimensionless variable range (b) Sensitivity index.

Please cite this article as: Kumar M et al., Numerical and experimental investigation to visualize the fluid flow and thermal characteristics of a cryogenic turboexpander, Energy, https://doi.org/10.1016/j.energy.2019.116267

M. Kumar et al. / Energy xxx (xxxx) xxx Table 2 The details of ANN model.

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Table 3 ANFIS network design.

Parameter

Value

Number of inputs Number of outputs Network structure Number of hidden layers Training algorithm Transfer function Error function Number of epochs Hidden neuron range

4 3 MLP 1 Back-propagation Logsig, Purelin, Tansig MAE 1000 1  10 with step size one

MFs type of input parameters MF type of output parameters Number of MFs Optimization method Number of training data Number of epochs

Gauss, Tri, Trap, Gbell Linear 4 Hybrid 54 200

parameters, specific speed, and specific diameter are used to determine the major dimensions of the turbine and its inlet and exit velocity triangles. The values are selected from the Balje chart in such a way that the Mach number of the fluid at the turbine inlet is in the subsonic regime and having maximum total-to-static efficiency which ultimately indicates the suitability of the design parameters.  Specific speed

ns ¼ 

Fig. 6. Schematic of ANN model network.

properties are complicated and varied at high-pressure and ultralow temperature. It is complicated to predict cryogenics fluid properties during the expansion process through ideal gas laws. Therefore, the accurate design of the turboexpander components needs a real gas model. Inlet pressure, mass flow rate, expansion ratio, rotational speed, blade speed ratio, flow angles and number of blades, etc. are the decision variables on which performance of the turbine depends. Pressure ratio ðrp Þ, velocity ratio ðvs Þ, hub and shroud exit radius to turbine inlet radius ratio are other parameters on which the feasibility of the turbine design depends. The ranges of these parameters are mentioned in Table 1. The 1-D design of turbine geometry is performed in Matlab® 2017b by adopting the analytical approach proposed by Hasselgruber and Balje using the basic primary data (thermodynamic properties) and some non-dimensional and geometrical parameters within the specified range [24]. The two dimensionless

w

pffiffiffiffiffiffi Q3 3=4

Dh23;s

(1)

 Specific diameter

ds ¼

   D2  Dh23;s 1 4 pffiffiffiffiffiffi Q3

(2)

where Q3 is the volumetric flow rate at the turbine exit and △h13;s is the isentropic enthalpy drop from inlet to the turbine exit. The next step is to select the degree of reaction, stage loading, flow coefficient ð4Þ and static head coefficient ðjÞ. The values of static head coefficient and flow coefficient are taken to be higher. The design procedure of an RIT and its velocity triangles are presented in Figs. 1 and 2.  Flow coefficient

Fig. 7. The basic structure of ANFIS.

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4¼

Cm3 Cm2 ¼ U2 cU2

(3)

 Static head coefficient

j¼

△h0 U 22

C C ¼ q2  l q3 U2 U2

limited to a maximum value of 0.70 to avoid excessive shroud curvature. The value of x is taken as 0.6, corresponding to the maximum efficiency within the subsonic zone and for obtaining longer blade passages.

x¼ (4)

where c represents the ratio of absolute meridional velocity at the inlet and outlet of the rotor and l is the outlet to inlet radius ratio of the turbine. Since RIT has maximum efficiency in the range of speed ratio of 0.62e0.70. The ratio of eye tip diameter to inlet diameter should be

Dtip D2

(5)

Kun and Sentz [25] have taken a hub ratio of 0.35 citing mechanical considerations. For the current design, the value of l is taken as 0.425. The number of blades is optimized in the range of 11  17, which is calculated as follows:

Z¼

p 30

ð110  a2 Þtanða2 Þ

(6)

Fig. 8. Regression curve of ANN (a) hts (b)Lt (c) P.

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Table 4 Comparison of variation of output parameters with different non-dimensional inputs and its prediction from ANN and ANFIS models. (a) Input and output parameters Input parameters

Output parameters

Rs = R2

Rh =R2

rp

vs

hts

Lt

PðkWÞ

0.92 0.89 0.86 0.85 0.86 0.9 0.90 0.85 0.8 0.91

0.25 0.27 0.25 0.28 0.22 0.25 0.25 0.26 0.26 0.26

3.10 2.62 2.89 3.14 4.20 2.68 3.42 3.44 3.68 4.14

0.62 0.62 0.68 0.72 0.73 0.74 0.70 0.69 0.66 0.65

0.802 0.821 0.823 0.836 0.778 0.769 0.802 0.803 0.784 0.816

0.22 0.188 0.178 0.188 0.241 0.256 0.181 0.165 0.187 0.154

0.608 1.331 3.191 0.465 1.345 1.289 1.780 1.724 2.169 2.815

(b) Predicted ANN results for different transfer functions LOGSIG

TANSIGhts

PURELIN

hts

Lt

P

hts

Lt

P

hts

Lt

P

0.802 0.820 0.823 0.820 0.784 0.794 0.804 0.806 0.788 0.811

0.218 0.186 0.179 0.188 0.241 0.221 0.180 0.169 0.185 0.158

0.607 1.281 3.201 0.482 1.575 1.308 1.794 1.778 1.986 2.838

0.802 0.817 0.825 0.817 0.798 0.79 0.813 0.805 0.784 0.814

0.201 0.203 0.188 0.173 0.187 0.197 0.170 0.177 0.209 0.163

0.698 1.212 3.159 0.492 1.735 1.399 1.712 1.640 1.920 2.737

0.805 0.817 0.825 0.808 0.799 0.792 0.801 0.808 0.787 0.809

0.221 0.188 0.168 0.187 0.241 0.204 0.176 0.172 0.194 0.158

0.707 1.241 3.061 0.485 1.499 1.478 1.751 1.648 1.871 2.682

(c)Predicted ANFIS results for different MFs Gauss

Training Errors Testing Error

TRI

TRAP

GBELL

hts

Lt

P

hts

Lt

P

hts

Lt

P

hts

Lt

P

0.802 0.821 0.823 0.836 0.778 0.78 0.802 0.804 0.784 0.816 0.193 0.736

0.219 0.193 0.174 0.162 0.171 0.18 0.162 0.171 0.195 0.162 0.012 0.721

0.612 1.249 3.221 0.453 1.351 1.308 1.761 1.696 2.163 2.792 0.431 0.694

0.802 0.821 0.823 0.836 0.778 0.78 0.802 0.803 0.784 0.816 0.230 0.954

0.22 0.188 0.178 0.163 0.173 0.183 0.163 0.173 0.195 0.163 0.019 0.793

0.638 1.391 3.248 0.478 1.371 1.157 1.724 1.701 2.362 2.743 0.80 0.968

0.802 0.821 0.823 0.836 0.778 0.78 0.802 0.803 0.784 0.816 0.196 0.872

0.22 0.186 0.18 0.164 0.24 0.187 0.164 0.183 0.20 0.155 0.020 0.737

0.619 1.286 3.221 0.476 1.362 1.303 1.744 1.739 2.348 2.943 0.619 0.741

0.802 0.821 0.823 0.823 0.778 0.78 0.802 0.803 0.784 0.816 0.198 0.894

0.205 0.191 0.182 0.165 0.182 0.191 0.165 0.182 0.205 0.165 0.022 0.743

0.641 1.216 3.092 0.491 1.357 1.340 1.688 1.813 2.181 2.841 0.793 0.866

After calculating the number of blades, the blade inlet angle ðb2 Þ and absolute flow angle ða2 Þ are determined. The thickness of the blade is obtained from the correlations proposed by Aungier [3]. The geometry of the turbine is presented in Fig. 3. The next step is to consider the different loss model in the design process. Based on these loss models, the total-to-static efficiency of the turbine is calculated which is used to update the initial guess. The losses are formulated as follows:

2.1.1. Incidence loss This loss is based on the principle of conversion of kinetic energy into internal energy of the fluid. It increases the entropy and formulated as follows:

" 2  # W 2 cos b2  b2;opt DhI ¼ 2 where b2;opt is the incidence angle which is defined as:

cot b2;opt ¼

1:98cotða2 Þ   Z 1  1:98 Z

(8)

2.1.2. Passage loss The passage loss is a function of mean kinetic energy. It is formulated as follows:

Dhpassage ¼ kp

!#  " 

Lh rt sinb3 W 22 þ W 23  þ 0:68 1   Dh r2 b3m =c 2



(9) (7)

where Lh , Dh and c are mean passage hydraulic length, diameter and turbine blade chord. kp is a constant which accounts the secondary losses. In this case, its value is taken as 0.2.

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Fig. 9. Decision surface of total-to-static efficiency ðhts Þ (a) Rs =R2 and Rh =R2 (b) vs and rp

2.1.3. Rotor clearance loss It is assumed that shear flow exists in the tip clearance. The velocity is varied linearly in this region approaching from zero in the vicinity of the casing to surface velocity on the blade. Therefore, axial ðεx Þ and radial ðεr Þ clearance of the turbine have major effects on turbine clearance loss which is formulated as follows:

DhCl ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U 22 Z kx εx Cx þ kr εr Cr þ kxr εx Cx εr Cr 8p

(10)

where kx and kr are the discharge coefficients in axial and radial directions respectively, kxr is the cross coupling coefficient. In this case, the values of kx , kr and kxr are taken to be 0.40, 0.75 and  0:3 respectively [26].

2.1.4. Trailing edge loss This loss has to be modeled by assuming that the relative pressure drop at the turbine exit is proportional to the relative kinetic energy.

Dprel ¼ p3rel  p2rel ¼

r3 W 23 2



Zt prt cosb3

(11)

This pressure loss is converted into loss coefficient formulated as:

DhTEL ¼

2

gM23rel



Dprel p3rel

(12)

2.1.5. Blade loading loss Blade loading losses are a kind of secondary loss obtained due to boundary layer separation. The curvature of the blade profile is also responsible for this type of loss. It is formulated as follows [27]:

DhBL ¼ 2

ðW2  U2 Þ2 ZL=r2

(13)

The total losses are formulated as:

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Fig. 10. Decision surface of total losses ðLt Þ (a) Rs =R2 and Rh =R2 (b) vs and rp

X

hLt ¼ DhI þ Dhpassage þ DhCl þ DhTEL þ DhBL

(14)

The total-to-static efficiency is updated with the addition of various losses as follows:

hts ¼

h0 P h0 þ hLt

(15)

Cqt ¼

C0 D 2 Dt

(17)

where Dt , Cmt and bt are throat circle diameter, meridian component of throat velocity and height of the nozzle. The nozzle height ðbt Þ is usually smaller than the turbine inlet blade height. This allows some margin for expansion in annular space and also accommodating the axial misalignment.

2.2. Design of nozzle The convergent type nozzle is used to provide the subsonic velocity at the nozzle exit. The meridional ðCmt Þ and throat ðCqt Þ are two velocity components obtained at the exit of the throat. Cmt is perpendicular to throat circle diameter, which determines the mass flow rate whereas Cqt is tangential to throat. The mass balance equation at meridional plane is as follows:

Cmt ¼

m

pDt rt bt

(16)

2.3. Sizing of the nozzle vanes The conservation of momentum and continuity equations are used for calculating throat angle which is directly related to trailing edge thickness of the nozzle. Aerodynamically, trailing edge thickness is as minimum as the mechanical design limit will allow. From the continuity equation, throat width ðWt Þ and throat angle ðat Þ are calculated as follows:  Throat width

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Fig. 11. Decision surface of power output (a) Rs =R2 and Rh =R2 (b) vs and rp

Wt ¼

mt Zn rt bt Ct

(18)

 Throat angle

at ¼ tan1



Cmt Cqt

 (19)

turbine depend. Besides, the design range of constants for RIT varies, static head coefficient ðjÞ varies from 0:82  0:90, flow coefficient ð4Þ is 0:20  0:28, eye tip ratio ðlÞ is 0:41  0:45, and hub ratio ðxÞ is 0:58  0:62. The variance decomposition, the total output variance to input constants are derived as follows:

VarðYÞ ¼

X

Di ðYÞ þ

X

Dij ðYÞ þ … þ D12…d ðYÞ

(20)

It is noted that the throat outlet angle is different from the turbine blade inlet angle and the inconsistency is due to the expansion of the fluid in the vaneless space.

where VarðYÞ is the total variance of total losses (output), Di ðYÞ is the first-order variance of input constants. Xi and Dij ðYÞ is the second-order variance of Xi and Xj which are formulated as:

2.4. Sensitivity analysis

VarðYÞ ¼ E Y 2i  E2 ðYi Þ

(21)

The Sobol method is applied for sensitivity analysis of the different constants because of its robustness and better reliability [28,29]. It affects the non-dimensional design variables and input constants on which total-to-static efficiency and total losses of the

Di ðYÞ ¼ Var½EðYjXi Þ

(22)

Thus, the first-order sensitivity index is written as follows:

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M. Kumar et al. / Energy xxx (xxxx) xxx Table 5 Comparison of present result with results available in literature. (a) Input parameters range Input parameters

Case 1

Fluid T02 ðKÞ P02 ðbarÞ Mass flow rate ðkg =sÞ a2 ðDegreeÞ Rotational speed ðrpmÞ

Nitrogen 90  180 8:0  10:0 0:01  0:09 72  82 80; 000  150; 000

11

the total losses is the highest ð14:35%Þ, that of 4 is second ð12:36%Þ, while those for x ð5:63%Þ and l ð3:69%Þ are very low. Fig. 5 represents the normalized sensitivity index of nondimensional design variables on total-to-static efficiency of the turbine. It shows that ratio of hub radius to turbine inlet radius ðRh =R2 Þ, pressure ratio ðrp Þ, ratio of shroud radius to turbine inlet radius ðRs =R2 Þ and speed ratio ðvs Þ has highest sensitivity on totalto-static efficiency as compared to specific speed ðns Þ and number of blades ðZÞ. Therefore, the optimal range of these variables has to accurately predicted.

(b) Output parameters (Comparison between present results and Ghosh et al. [30])

d2 ðmmÞ d3 ðmmÞ b2 ðmmÞ b3 ðmmÞ U2 ðm =secÞ U3 ðm =secÞ

j

4

hts htt b2 ðDegreeÞ b3 ðDegreeÞ

M2 M3 ns Total losses ðLt Þ Power ðkWÞ

Present results (Model 1/Model 2)

Ghosh et al.

Relative error

24.90/25.64 15.60/15.71 2.11/2.14 1.005/1.01 143.38/144.62 124.42/122.73 0.862/0.87 0.237/0.24 79.20/79.41 80.20/79.89 54:98 /  55:12 85:04 /  84:76 0.78/0.79 0.25/0.28 0.54/0.55 0.226/0.208 3.52/3.49

25.19 15.75 2.00 0.996 130.28 121.88 0.88 0.241 76.10 77.51  69:78  85:74 0.85 0.31 0.47 0.242 2.83

0.012/0.018 0.01/0.003 0.06/0.07 0.009/0.014 0.09/0.09 0.02/0.01 0.02/0.01 0.017/0.004 0.04/0.04 0.03/0.03 0.21/0.21 0.01/0.01 0.08/0.07 0.194/0.097 0.13/0.15 0.06/0.14 0.196/0.189

Parameters

Model 1

Model 2

Turbine diameter at inlet ðmmÞ Turbine diameter at outlet ðmmÞ Number of blades ðZÞ Pitch circle diameter of nozzle ðmmÞ Outlet diameter of nozzle ðmmÞ Number of nozzles ðZn Þ

24.90 15.60 13 40.14 25.58 20

25.64 15.71 11 40.25 25.73 17

Table 7 Specification of measuring components. Parameters

Instrument

Accuracy

Company

Pressure Temperature Mass flow rate Rotational speed

Pressure transducer RTD scanner, ADAM Rotameter Speed sensor

±0:2% 80  600 K ±2:5%: ±0:005%

Endevco Santronix Alflow Micro-Epsilon

Di ðYÞ VarðYÞ

The ANN and ANFIS are soft computing models which are developed using the non-dimensional design variables of an RIT to predict its optimal ranges in which it has the highest performance. The ANN is an adaptive system used as a simulation and prediction tool, motivated by the biological neural network of the human brain. The models are developed to predict the total-to-static efficiency, total losses, and power output of RIT with a set of design variables in Matlab® toolbox. The present model has four input parameters (Rs =R2 , Rh =R2 , vs and rp ) and three output parameters (hts ; Lt and P).

3.1. ANN model development

Table 6 Essential parameters of the radial inflow turbine.

Si ¼

3. ANN and ANFIS network development and predicted results

(23)

To analyze the sensitivity of different constants, the total losses are computed by fixing one parameter and changing the other parameters. These results are shown in Fig. 4, in which the values of D equals to the normalized range of the input parameters. As represented, the effect of constants on the total losses shows negative growth. It is observed that the first-order sensitivity index of j on

The number of layers, neurons, and transfer function type are identified in the ANN model. The multi-layer perceptron (MLP) neural network with a single hidden layer has opted for training process using back-propagation algorithm. Three transfer functions (TFs) are used for a comparative study of data prediction in hidden as well as the output layer. From several trials, the best network is obtained by varying the hidden neurons in the range of 1e10. For every hidden neuron, the training process is repeated. The additional details of the ANN model are mentioned in Table 2. Initially, the datasets are divided into three parts (training, testing and validation datasets containing 80%, 10%, and 10% respectively). The training data train the network, the validation datasets tests the accuracy of the network. The final model with high prediction accuracy rate has opted in which optimized input and output datasets are determined. Fig. 6 represents a schematic of an MLP with a single hidden layer. Every unit in the network is connected with a node in the very next layer. The input parameters are given to the network; it multiplies with the weight of the hidden neurons. The weighted input values are summed up and transformed when it passes through the hidden neurons. The output of the hidden layer is the input of the next layer, and the process is continued in a forward direction. The functional relation is expressed as follows:

ym ¼ g

k X j¼0

w2mj f

n X

w1ji xi



(24)

i¼0

where n is number of input neuron, k is the hidden neurons and ym is the output neuron.

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Fig. 12. Schematic diagram of the experimental set-up.

and Table 3. 3.3. ANN and ANFIS results

Fig. 13. Experimental set-up.

3.2. Structure of adaptive neuro-fuzzy inference system Membership functions (MFs) are determined to establish an ANFIS network. There are various membership functions available, but for the present case, Gauss, Tri, Trap and Gbell MFs are employed for input parameters and compare the mean absolute error (MAE). For the output parameters, a linear function has opted. The basic structural information of ANFIS network is shown in Fig. 7

Fig. 8 illustrates the comparison of the regression of calculated and predicted total-to-static efficiency, total losses, and power output. Initially, the ANFIS networks are trained based on the input variables used in the designing process. There are three networks: ANFIS-1 estimate the total-to-static efficiency, ANFIS-2 estimate the total losses, and ANFIS-3 estimate the power output. Four different type MFs (Gauss, Tri, Trap, and Gbell) are used during the training process out of which Gauss MF possess less error (Table 4 (c)). Therefore, decision surfaces obtained from Gauss MF are presented hereafter. The final decision surfaces obtained from ANFIS training are represented in Figs. 9e11. It illustrates that the total-tostatic efficiency of the turbine is higher when Rs =R2 and Rh =R2 are in the range of 0:80  0:87 and 0:24  0:27 whereas velocity ratio ðvs Þ and pressure ratio ðrp Þ are in the range of 0:65  0:68 and 3:30  3:80 respectively. In this range, the power output is on the higher side which is directly related to the refrigerating capacity of the turbine. But the total losses are at a lower side in these zones. Therefore, we select these ranges for better performance of the turbine. The samples of non-dimensional input and output parameters and its predicted output values are summarised in Table 4. 3.4. Mean-line design results and its validation Based on the aforementioned design methodology and optimal ranges of non-dimensional variables, the obtained dimensions are compared with available data which is mentioned in Table 5. It indicates that except turbine exit Mach number ðM3 Þ and power

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Fig. 14. (a) Components of a turboexpander (b) Three-dimensional drawing in Solidworks.

Table 8 Node distribution and its scheme in different blocks of the turbine (Model 1=2). Inlet block

Turbine Nozzle

Outlet block

Passage block

Streamwise

Blade-to-blade

Streamwise

Blade-to-blade

Streamwise

Blade-to-blade

22=20 16/16

50=50 35/36

25=26 14/14

50=54 34/32

80=85 54/54

40=42 28/28

Table 10 Grid independence analysis (Model 1=2). Table 9 Non-dimensional wall distance of the turbine and nozzle (Model 1= 2). Sections

yþ value

Sections

yþ value

Turbine inlet Near turbine blade Center of the flow passage Turbine outlet

8=8 3=3 14=14 20=20

Nozzle inlet Near Nozzle blade Center of the flow passage Nozzle outlet

10=10 5=5 18=18 15=15

Nozzle (Nodes in Million)

Turbine (Nodes in Million)

Isentropic efficiency

CPU time (hrs)

0:48=0:49 0:64=0:68 0:72=0:75 0:85=0:89

0:81=0:80 0:96=0:99 1:11=1:12 1:24=1:26

0:68=0:73 0:72=0:76 0:75=0:79 0:76=0:80

142=140 146=149 151=153 156=159

output ðPÞ, other variables show good agreement. The variation

Fig. 15. Computational domain of nozzle and turbine.

Fig. 16. Selected grid size for turbine and nozzle (a) Model 1 (b) Model 2.

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Fig. 17. Experimental validation of numerical results (a) pressure ratio (b) isentropic efficiency with mass flow rate.

Table 11 Statistical data of experimental and numerical results (Experimental/Numerical). m_ (kg/s)

rp

% deviation from numerical

his

% deviation from numerical

0.085 0.08 0.073 0.069 0.065 0.061 0.056 0.052 0.047 0.042 0.039 0.033 0.028 0.026

4:67=4:70 4:63=4:67 4:61=4:63 4:40=4:52 4:26=4:48 4:09=4:37 3:98=4:23 3:95=4:09 3:81=3:90 3:64=3:78 3:42=3:61 3:35=3:50 3:25=3:32 3:01=3:08

0.64 0.86 0.43 2.65 5.16 6.41 5.91 3.54 2.31 3.85 5.26 4.29 2.10 2.27

0:71=0:73 0:74=0:75 0:76=0:78 0:78=0:80 0:79=0:80 0:78=0:79 0:74=0:75 0:72=0:73 0:66=0:70 0:65=0:68 0:60=0:61 0:51=0:54 0:52=0:55 0:53=0:54

2.74 1.33 2.56 2.50 1.25 1.26 1.33 1.37 5.71 4.41 1.64 5.56 5.55 1.85

occurs due to increase in specific speed ðns Þ which is selected from Balje ns  ds diagram. Due to this, power output increases which have a significant effect on refrigerating capacity of the turbine. Also, decrease in turbine exit Mach number ðM3 Þ reduces kinetic energy loss (trailing edge loss). In this way, two turbine models are developed. The first one is for an inlet temperature of 120K and 130K (model 1) and the second one is for 140K and 150K (model 2). Assuming good agreement with Ghosh et al. [30], one can use the 1  D approach to obtain a reasonable design condition. Other important turbine and nozzle specifications are mentioned in Table 6.

4. Experimental test-rig development The experimental test-rig consists of a compressed air facility (KAESER SIGMA BSD 72), purification and filtration unit, precooler, turboexpander set-up, plate-fin heat exchanger (PFHX), a reservoir, and different safety and monitoring instruments. The heat exchanger and turbine supply line is connected with flexible stainless steel hose pipe (Grade SS304) and flow is controlled through regulating valve. Firstly, the compressed air passes through three-layer filtration and purification unit in which carbon molecules, dust particles, water and oil molecules are removed. This process is essential to avoid the failure of aerodynamic bearings and decrement of performance of turboexpander. Secondly, a freon cooler is situated in which the temperature of the compressed air is reduced and delivered dry and dehumidified air. After that, the high-pressure supply line passes through plate-fin heat exchanger (PFHX) [31] in which liquid nitrogen is supplied to achieve the cryogenic

Table 12 Statistical data of experimental and numerical results (temperature drop). Rotational speed

Experimental

Numerical

% deviation from numerical

27.2 23.8 21.5 17.6 15.6 13.8

29.8 26.1 24.8 20.5 18.1 15.6

8.72 8.81 13.31 14.15 13.81 11.54

(103 RPM)

Fig. 18. Effect of rotational speed on temperature drop.

119 115 112 106 95.1 84.3

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Fig. 19. Pressure contours at 0.50 span for model 1.

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Fig. 20. Pressure contours at 0.50 span for model 2.

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ANSYS® Turbo-Grid. The H-type topology is used for inlet and outlet blocks whereas J/O-type is selected for the passage block to solve the near-wall region which is required for boundary layer flow visualization. The node distribution of the grid and its schemes are mentioned in Table 8. The O-grid (20) includes in the periodic boundary and 100 points are located from hub to shroud. Also, the yþ value which shows the non-dimensional distance from the wall is mentioned in Table 9.

5.2. Numerical methods and turbulence model

Fig. 21. Area-averaged density variation along the streamwise location.

temperature. In this way, high-pressure and low-temperature fluid is available for testing the performance of turboexpander. The experimental test-rig have extended measuring point. The inlet pressure, temperature, and mass flow rate to the turboexpander unit is measured with a pressure gauge, ADAM, and rotameter respectively. Also, the turbine tip pressure is measured using pressure transducer. The rotational speed of the turbine is measured using eddy current sensor and oscilloscope. The specifications of measuring components are mentioned in Table 7. The schematic diagram and images of important components used in the development of the experimental test-rig are shown in Figs. 12e14. The turbine blade profile is designed to operate at a rotational speed of 60; 000  120; 000 rpm (approximately 40%e80% of the designed rotational speed). The aerodynamic gas bearings are used to reduce the axial force on the shaft. Additionally, a brake compressor mounts on the same shaft to dissipate the power generated by the turbine. This provides the refrigerating capacity of the turboexpander. The turboexpander assembly is placeed inside the bearing housing (160 mm external diameter and 157.50 mm height) and make it leak-proof using O-ring (Fig. 14 (a)). The shaft and brake compressor is made of chromium-vanadium steel whereas the other stationary components are made of stainless steel. The turbine is made of aluminum alloy (Al 6082). Initially, the compressed air is supplied to the aerodynamic journal and thrust bearings instead of driving the turbine. The bearing pressure is maintained to be 5 bar. After that, the working fluid is supplied at different mass flow rates to turboexpander unit. 5. Numerical issues and boundary conditions 5.1. Computational model and mesh generation For high computational accuracy of the results, fine hexahedral grids are generated for the turbine and nozzle models using

The numerical simulations are conducted using commercially available CFD platform ANSYS® CFX. It is based on the threedimensional, time-dependent, viscous and compressible Reynolds Averaged Navier-Stokes (RANS) equations using finite volume method. The high-resolution scheme opts for the discretization of the advection term and turbulent viscosity term whereas the second-order upwind scheme is used for spatial discretization. For transient rotor-stator solutions, second-order backward Euler scheme is used. The generalized grid interface (GGI) is selected at the interface to connect the turbine and nozzle for stage analysis. The dynamic model control of solver is achieved using automatic pressure level information, temperature damping, velocity pressure coupling, and Rhie-Chow fourth-order model. Medium turbulence (5%) intensity is used at the inlet boundary. Transient simulations are run using the passing period option and maximum number of iteration loops are fixed to be 10. The simulations are assumed to be converged when normalized RMS residuals are less than 106 . The conservation target is set to be 105 . Firstly, a moving reference frame is defined using a frozen rotor with automatic pitch change model to compute the rotation of turbine in steady-state condition. In this method, the fluid around the blade is set as a moving reference frame whereas the blade and hub are assumed to be stationary with respect to the inner fluid. In this way, there is no need for grid movement during the steadystate simulation. Secondly, a sliding mesh method is performed to simulate the rotation of the turbine during transient blade row simulation. Therefore, the transient rotor-stator boundary condition is imposed at the interface of the two domains. The rotor inner domain rotates at each time step which is defined by the rotational speed and pitch ratio. Thus the boundary nodes of stator and rotor domain slide with respect to each other. This methodology is realistic and more demanding to simulate the flow in turbomachinery problems [32]. The steady-state solutions are used as an initial solution for a transient rotor-stator simulation for faster convergence. It takes about 150 h to attain a converged solution using Intel®Xeon®CPU E5-1660 v3 @ 3.00 GHz with 64 GB RAM. For the present study, Shear Stress Transport (SST) k  u turbulence model is opted to capture turbulence closure and flow separation effects on the eddy viscosity. This turbulence model can accurately predict the turbomachinery flows having boundary layer separations. It combines the advantages of two commonly used turbulence models: k  u model and k  ε model. k  u model can predict the flow near-wall region whereas k  ε model in wakes and free-shear regions in the outer boundary layer (bulk flow). A blending function establishes a smooth transition between two models. In this aspect, k  u SST model can predict the boundary layer through the passage (excellent turbulent boundary layer modeling behavior), in which u near the wall is more stable than that of ε. Due to these assimilating features, it can accurately predict

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Fig. 22. Mach number contours at 0.50 span for model 1.

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Fig. 23. Mach number contours at 0.50 span for model 2.

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Fig. 24. Velocity vectors of model 1 at different spans.

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the turbomachinery flows having boundary layer separations [33]. The implementation of the equation of state significantly affects the accuracy of the numerical solution. Therefore, the Peng-Robinson model is selected in the numerical simulation [34]. 5.3. Boundary conditions Fig. 15 illustrates the boundary details of the computational domain. The numerical simulations are done using the following boundary conditions:  Inlet: Total pressure (8 bar), total temperature (120, 130, 140, and 150 K), flow direction (normal to boundary) and rotational speed are imposed at the inlet boundary.  Outlet: Static pressure is chosen at the outlet boundary.  Periodic boundary conditions: Circumferential periodic boundary conditions are used for sidewalls along the pitchwise direction which shows the physical condition (rotating or stationary) of each blade row.  The walls (hub, blade, shroud, etc.) are assumed to be adiabatic, hydraulically smooth, and no-slip condition.

5.4. Grid independence test To validate the accuracy of numerical results, a grid independence test is carried out. In this work, four grid resolutions for both the models are used to discretize the computational domain. The isentropic efficiency and computational time for obtaining a converged solution are compared which are mentioned in Table 10. It is observed that among the four investigated grid resolutions, the difference in the isentropic efficiency of the third and fourth row is least. After that, the computational time is increased with less effect on the isentropic efficiency. Therefore, as a compromise between the accuracy of the results and computational time, the third row of Table 10 has opted for the remainder of the analysis as shown in Fig. 16. 6. Results and discussions 6.1. Experimental validation of the numerical results

Fig. 25. Velocity vectors for model 2 at different spans.

A series of experiments have been performed to investigate the performance of a reversed Brayton cycle-based air turboexpander. The numerical results are validated with the experiments by operating the turboexpander unit at the off-design condition. Fig. 17 represents the comparison of experimental and numerical results of pressure ratio and isentropic efficiency variation with mass flow rate. It is observed that the pressure ratio increases with the increase in mass flow rate. However, some deviations in pressure ratio are detected because of experimental uncertainty error. The isentropic efficiency increases up to the mass flow rate of 0.04 kg/s after that it decreases with the increase in mass flow rate. The maximum isentropic efficiency is obtained at a pressure ratio in the range of 3:3  3:8. It means that the isentropic efficiency increases with an increase in pressure ratio up to the mass flow rate of 0.04 kg/s. After that, the isentropic efficiency decreases with an increase in pressure ratio. The percentage deviations of experimental and numerical results at different mass flow rates are mentioned in Table 11. Fig. 18 illustrates the effect of the rotational speed of the turbine on temperature drop. It is noted that the temperature drop increases with the increase in rotational speed. However, there is some variation in temperature drop between experimental and numerical results. Since the numerical simulations are carried out

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Fig. 26. Static entropy contours at 0.50 span for model 1.

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Fig. 27. Static entropy contours at 0.50 span for model 2.

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Fig. 28. Variation of Reynolds number along the streamwise location.

assuming adiabatic boundary condition but practically it is not possible to create the adiabatic condition inside the turboexpander. Because of this, the variation in temperature drop is obtained. The percentage deviation of experimental results from the numerical analysis is mentioned in Table 12.

6.2. Effect of pressure variation on the fluid flow properties The fluid flow characteristics inside the nozzle and turbine are three-dimensional and completely different because of variation in density and viscosity of the fluid at cryogenic temperature. Therefore, it is essential to compare the flow properties of the fluid under these conditions for significant use in a turboexpander. Figs. 19 and 20 represent the pressure contours, obtained from the two different models. The contours are presented at 50% blade height (span). The nozzle is designed in such a way that the maximum pressure drop is approximately 1.2 bar. This pressure energy is converted into the kinetic energy due to which the desired Mach number is obtained at the nozzle exit. The pressure drop inside the turbine is approximately 2.24. It is also noticed that the fluid inlet temperature also affects the pressure variation inside the nozzle and turbine. It happens because of severe changes in density and molecular viscosity of the cryogenic fluids at high pressure and ultra-low temperature (Fig. 21). The fluid velocity increases due to pressure drop along the downstream direction. Figs. 22 and 23 illustrate the Mach number distribution at 0.50 span. It indicates that the Mach number at the outlet of the nozzle is in the subsonic regime which is important for flow stability at the inlet of the turbine. It is observed that the Mach number at the outlet of the nozzle is highest for inlet temperature of 120 K (model 1). The adverse pressure gradient along the downstream direction is responsible for flow separation inside the turbine which is represented in Figs. 24 and 25. The secondary flow occurs in the vicinity of the blade wall boundary layer because of the relatively higher radial component of Coriolis acceleration as compared to the

radial pressure gradient. This phenomenon is also observed by Zangeneh et al. [35] for the centrifugal impeller. The secondary flow also appears due to the induced pressure gradient by the curvature of the blade profile. Fig. 25 also depicts that the passage vortices occur at 0.20 and 0.50 span near the leading edge, it is disappeared with the interaction of the mainstream fluids. At higher span, the vortices are completely disappeared. The tip leakage flow introduces the non-uniformity and turbulence in the fluid flow and a major cause of losses in the rotating machines. It is observed that tip leakage flow occurs near the leading edge in model 1. For model 2, it occurs in the middle portion and starts changing its direction. The boundary layer formation and free stream layer impose the increase in entropy (Figs. 26 and 27). The viscous friction increases due to the generation of vortices in the flow passage which also increase the entropy of the fluid. It may also happen due to the mixing of fluid streams from pressure and suction side of the blade, increases the shear strain which leads to increase the entropy in model 2. Fig. 28 illustrates the variation of the Reynolds number along with the streamwise location. It is observed that Reynolds number is maximum for 120K and 150K fluid near the turbine inlet. For the remaining part, the variation is approximately similar.

6.3. Effect of pressure variation on the thermal properties Figs. 29 and 30 illustrate the temperature variation of the working fluid at four different inlet temperatures. The contours show that the temperature drop is approximately 20, 24, 27 and 30 K for 120, 130, 140 and 150 K inlet temperature fluids at 8.00 bar inlet pressure. The higher temperature drop is essential at cryogenic temperature because it increases the efficiency of the system. It is also noted that the temperature drop is maximum for 150 K inlet temperature. It happens because of a relatively higher static enthalpy drop of the fluid at higher cryogenic temperature (Fig. 31 (a)). For other cases, the temperature drop decreases due to fluid approaches nearer to its boiling point. In those cases, the thermodynamic properties of the cryogenic fluids are randomly changed which severely affect the fluid flow and thermal behavior during the expansion process. Generally, for normal expansion process, the temperature and enthalpy drop depends on the pressure change, but at the cryogenic temperature, it severely dependent on the fluid state and its properties. The high-temperature nitrogen (case 4) contains higher enthalpy as compared to other cases at the same pressure. During the expansion stage, it decreases at a relatively higher rate due to which a higher temperature drop exists (Fig. 32). The expansion process inside the turbine and nozzle is generally based on the throttling or adiabatic effect premise. In this regard, the process can be explained based on the pressure-static enthalpy (p-h) and temperature-static entropy (T-s) variation of the fluid as represented in Fig. 33. The law of conservation of energy states that the pressure energy is converted into kinetic energy of fluid during the expansion process. During the energy conversion process, the velocity of fluid increases and enthalpy decreases, as a result, temperature drop takes place. Since the actual expansion process is different from the ideal process because of an increase in entropy of the fluid (Fig. 31 (b)). Therefore, isentropic efficiency ðhis Þ is considered to assess the irreversibility during the expansion process. The isentropic efficiency is calculated as:

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Fig. 29. Temperature contours at 0.50 span for model 1.

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Fig. 30. Temperature contours at 0.50 span for model 2.

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Fig. 31. Area-averaged (a) Static enthalpy (b) Static entropy variation along the streamwise location.

6.4. Effect on TKE and eddy viscosity The turbulence kinetic energy (TKE) is measured to visualize the intensity of turbulence and eddy viscosity in the fluid flow. It considerably depends on the flow characteristics, the profile, and the free-stream turbulence intensity. The turbulence in the fluid flow can be determined with eddy viscosity by concerning to eddy diffusion and its distribution. Fig. 35 illustrates the TKE variation along with the streamwise location. It shows that the intensity of TKE is almost negligible for all the cases in the nozzle as compared to that of the turbine. Since the flow inside the turbine is turbulent, the intensity of TKE increases up to 1.2 streamwise location. After that, the variation occurs due to the curvature of the blade profile. The maximum TKE is obtained for 150K inlet temperature (case 4). Figs. 36 and 37 illustrate the variation of eddy viscosity at 0.50 span. It is noted that the intensity of eddy viscosity is less for case 1 and 2. Although, its intensity is highest near the leading edge and decreases towards the trailing edge where the turbulence stabilizes and the losses are minimum. 7. Conclusion Fig. 32. Area-averaged temperature variation along the streamwise location.

his ¼

h1  h3 h1  h3;is

(25)

The isentropic efficiency and power output of the system for different inlet temperature of the fluids are mentioned in Table 13. The ideal gas properties of the fluid are obtained from the REFPROP at corresponding pressure and temperature. Prandtl number is a dimensionless parameter to distinguish the thermal condition of the fluid at different inlet temperatures. Fig. 34 illustrates the Prandtl number variation inside the turbine and nozzle which depicts the thermal condition of the fluid at different temperatures.

The present research focuses on the systematic design methodology for the development of the radial turbine and nozzle by considering different loss models and validate the obtained results with the available data. Sobol sensitivity analysis is carried out to explain the effect of various constants on total losses and nondimensional design variables on total-to-static efficiency of the turbine. The research is further extended to predict the optimal range of non-dimensional design variables through artificial intelligence methods (ANN and ANFIS). One-dimensional results show that the designed turbine exhibits an increase in total-to-static efficiency and power output by 4% and 18:9% respectively. Thereafter, numerical simulations are performed to characterize the flow field and thermal behavior at different spans and streamwise location. The numerical result of one case study is also validated with the experimental results to check the reliability of the

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Fig. 33. (a) Pressure Vs static enthalpy (b) Temperature Vs static entropy variation along the streamwise location.

Table 13 Efficiency of the turboexpander for different cases (1-D/Numerical). S. No.

Isentropic efficiencyðhis Þ

Power ðkWÞ

Case Case Case Case

0:771=0:722 0:771=0:765 0:813=0:783 0:813=0:801

3:15=2:87 3:15=3:04 3:39=3:24 3:39=3:36

1 2 3 4

Fig. 35. Area-averaged turbulence kinetic energy variation along the streamwise location.

Fig. 34. Variation of Prandtl number along the streamwise location.

respectively. The temperature drop (approximately 30 K) is maximum for an inlet temperature of 150 K due to the higher enthalpy drop. Furthermore, the scraping flow, flow separation, vortices, etc. at different spans of the turbine is visualized. The numerical results determine the capability of the numerical investigation to visualize the fluid flow and thermal characteristics of a nozzle and turbine. It is believed that the proposed work is quite beneficial for the development of an experimental prototype of a cryogenic turboexpander.

numerical solution. It is observed that the isentropic efficiency of the turboexpander is maximum when the mass flow rate and pressure ratio are in the range of 0:03  0:05 kg/s and 3:90 4:42

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Fig. 36. Eddy viscosity contours at 0.50 span for model 1.

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Fig. 37. Eddy viscosity contours at 0.50 span for model 2.

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Declaration of competing interest The authors declared that there is no conflict of interest to any person or organisation. Acknowledgements The authors sincerely thank Board of Research in Nuclear Sciences (BRNS), Ministry of Human Resource Development ðMHRDÞ, Government of India, and National Institute of Technology, Rourkela for providing the financial support. The authors present immense gratitude to Prof. Ashok K. Satapathy (Professor, NIT, Rourkela) who supports and continuously discuss with us on this regard. We are also grateful to the senior technicians of our institute Mr. Somnath Das and Mr. Sudhananda Pani for delivering valuable suggestions during commissioning of the experimental set-up and helping us in the experiments. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.energy.2019.116267. References [1] Reif-Acherman S. Several motivations, improved procedures, and different contexts: the first liquefactions of helium around the world. Int J Refrig 2009;32(5):738e62. [2] Whitfield A, Baines NC. Design of radial turbomachines. 1990. [3] Aungier RH. Aerodynamic design and performance analysis of exhaust diffusers. ASME press; 2006. [4] Khalil KM, Mahmoud S, Al-Dadah R, Ennil AB. Investigate a hybrid openRankine cycle small-scale axial nitrogen expander by a camber line control point parameterization optimization technique. Appl Therm Eng 2017;127: 823e36. [5] Suhrmann JF, Peitsch D, Gugau M, Heuer T, Tomm U. Validation and development of loss models for small size radial turbines. In: ASME turbo expo 2010: power for land, sea, and air. American Society of Mechanical Engineers; 2010. p. 1937e49. [6] Ennil AB, Al-Dadah R, Mahmoud S, Rahbar K, AlJubori A. Minimization of loss in small scale axial air turbine using CFD modeling and evolutionary algorithm optimization. Appl Therm Eng 2016;102:841e8. [7] Carter C, Guillot S, Ng W, Copenhaver W. Aerodynamic performance of a highturning compressor stator with flow control. In: 37th joint propulsion conference and exhibit; 2001. p. 3973. [8] Denton JD. Loss mechanisms in turbomachines. In: ASME 1993 international gas turbine and aeroengine congress and exposition. American Society of Mechanical Engineers; 1993. pp. V002T14A001eV002T14A001. [9] Ventura CA, Jacobs PA, Rowlands AS, Petrie-Repar P, Sauret E. Preliminary design and performance estimation of radial inflow turbines: an automated approach. J Fluids Eng 2012;134(3):031102. [10] Klonowicz P, Heberle F, Preißinger M, Brüggemann D. Significance of loss correlations in performance prediction of small scale, highly loaded turbine stages working in Organic Rankine Cycles. Energy 2014;72:322e30. [11] Salahshoor K, Kordestani M, Khoshro MS. Fault detection and diagnosis of an industrial steam turbine using fusion of SVM (support vector machine) and ANFIS (adaptive neuro-fuzzy inference system) classifiers. Energy

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Please cite this article as: Kumar M et al., Numerical and experimental investigation to visualize the fluid flow and thermal characteristics of a cryogenic turboexpander, Energy, https://doi.org/10.1016/j.energy.2019.116267