OPTIMIZATION OF THE HEAT TRANSFER AND PRESSURE DROP CHARACTERISTICS OF TRIPLE CONCENTRIC TUBE HEAT BY RESPONSE SURFACE METHODOLOGY (RSM)
APPROACHES Jasvant Singh Sisodiya
Department of Mechanical Engineering, BM College of Technology, RGPV, Bhopal Professor Purushottam Kumar Sahu
Department of Mechanical Engineering, BM College of Technology, RGPV, Bhopal Abstract - In this section, the simulation results of thermo hydraulic performance have been used to determine the optimum condition based on the considered range of the design parameters. The primary aim is to develop a functional correlation (relationship) between
‘‘input variables’’ (Reynolds number and length to hydraulic diameter ratio) and ‘‘the response’’ (Nusselt number and Friction factor) using Response surface methodology (RSM).
The Nusselt number and friction factor results obtained from CFD has been used for the same. Results of the present work has been validated with published experimental work in the literature. 19
Index Terms: Cylindrical grinding Taguchi method Alloy steel EN9 Material removal rate.
1INTRODUCTION
The inner annulus has 2 heat exchange surfaces (inner tube outer surface and outer tube inner surface) that will increase the heat exchange area of heat exchanger marginally compared to double tube device (has just one heat exchange surface) which will increase the speed of heat exchange. It conjointly in terms will increase the potency of heat exchanger. Therefore, it conjointly decreases the length of desired heat changer for constant temperature distinction compared to double tube devices. In the case of the double tube heat exchanger, the possible flow configurations are parallel flow and counter flow. In regards with the triple tube heat exchanger (TTHE), there are three fluids flowing resulting four possible configurations.
Comparison of the above configuration results in eight possible flow configurations.
In the recent years, triplex concentric tube heat exchangers gained a lot of interest for the PCM based heat exchanger.
This type of heat exchanger has three concentric tubes out of which middle tube is filled with PCM. Through inner and outer tubes heat transfer fluid is passed, so the PCM melts at a faster rate as the heat transfer fluid flows on both sides of the PCM. An added advantage of this type of heat exchanger is that it can be used for simultaneous charging and discharging.
Here the hot fluid is allowed to pass through one side of PCM and cold fluid through the other side. The studies related to triplex tube heat exchangers can be divided into two subsections. The first subsection discusses the parametric
investigation and the second one about the studies related to heat transfer enhancement. It can be noted that the details pertaining to TCTHX available in the literature is limited to horizontal orientation. Therefore, the discussions for TCTHX provided in subsequent sections correspond to horizontal orientation. The physical configuration of the triplex concentric tube heat exchangers shown in Fig. 1 and this model was first proposed by Long and Zhu [1].
Fig. 1 Schematic of triple concentric tube heat exchanger a) Charging or
discharging mode b) simultaneous charging and discharging mode. [18]
1.1 Computational Domain
A Triple concentric-tube heat exchanger and its computational domain are shown in Figure 1. The exchanger consists of three tubes such that the hot fluid flows through the inner annulus whereas the cold fluid and the intermediate temperature fluids flow through the inner tube and outer
annulus, respectively. Pure water with the flow rate ranging from laminar to turbulent has been used in all the three passages.
The detail geometrical description of the heat exchanger is given in Table 1.
Figure 1 Schematic representation of Triple Concentric-tube Heat exchanger
and its Computational domain. [19]
Table 1 Geometrical and boundary conditions.
Geometry Inner tube Inner
annulus Outer annulus Inner
diameter[m] D1i= 0.01 D2i=
0.022 D3i= 0.033 Outer
diameter[m] D1o=0.012 D2o=
0.024 D3o=
0.036 Thickness, t[m] 0.001 0.001 0.0015 Hydraulic
diameter, Dh[m] 0.01 0.01 0.009
Length, L [m] 1.41 1.41 1.41
Boundary conditions
Fluid stream Inlet Outlet
Cold fluid Velocity inlet Tin =300C (303K)
Pressure outlet Hot fluid Velocity inlet
Tin =600C (333K) Pressure outlet Intermediate
temperature fluid Velocity inlet Tin= 400C (313K Fluid-wall
interface Coupled /conjugate heat transfer
Outer wall No-slip condition and Insulated
Figure 2 Schematic diagram of the triple concentric-tube heat exchanger [20]
Figure 4 Flow patterns for the triple tube heat exchanger [20]
Figure 5 The approached method of the average LMTD [20]
2 METHODOLOGY
2.1 Numerical Procedure
In this section, the preliminary numerical simulation of heat transfer and pressure drop of triple concentric tube heat exchanger has been discussed. Initially, the simulation has been conducted for a fixed geometry of the heat exchanger (length to hydraulic diameter ratio, L/Dh=140) and Re: 2500–10,000. The heat transfer and pressure drop results of this simulation were documented. Later the simulation has been extended for varying length to hydraulic diameter ratio: L/Dh=100, 180,220. Two possibilities of varying/Dh can be considered here; varying either the length or hydraulic diameter one at a time.
In the present work, the length of the tube was allowed to vary in such a way that the non-dimensional factories maintained at the above-mentioned values.
This offers additional advantage of studying the individual effects of each parameter as well as uniformity of the analysis. In the subsequent simulations, the heat transfer values of the previous
simulation have been used. In doing so, the effect of varying geometry and flow rate on the thermo hydraulic performance of triple concentric-tube heat exchanger can be studied
2.2 Governing Equations and Boundary Conditions
The flow and heat transfer for the hot fluid flowing in the inner annulus were defined by conservation equations of mass, momentum and energy. Heat transfer occurs among the fluids through the walls separating them. The governing equations in a generic form including continuity, momentum and energy equations as well as turbulence model can be expressed in tensor notation as follows.
∇. (𝜌𝑉 𝜑) = ∇. (𝜏∅∇∅ + 𝑆∅
Where the terms 𝜏∅ and 𝑆∅represent the appropriate diffusion and source terms, respectively. The details of the governing equations are available in published work.
2.3 Solution Procedure
The commercial CFD package ANSYS Fluent v17.0has been used to solve the present problem. Second or drop wind differencing scheme with SIMPLE algorithm was applied to solve the convection terms.
Convergence criteria for all equations were set at10_6. RNG k-" model is adopted for turbulence modelling it offers better capturing near critical zones. A point implicit (Gauss-Seidel) linear equation solver along with an Algebraic multi-grid (AMG) has been applied to solve the resulting linear systems.
2.4 Data Reduction
The quantitative analysis of thermo hydraulic performance is performed based on the approach followed in literature.17 the heat transferred from the hot fluid through inner annulus
Qh = (mCp) h (Ti -To) h
The heat transferred to the cold fluid in the inner tube
QC= (mCp) c (To-Ti) c
The heat transferred to the intermediate temperature fluid in the outer annulus
Qi = (mCp) i (To-Ti) i
Thus, the average heat transfer among the three fluids can easily be given as
Qav=[Qh +Qc +Qi ] 2
Further, the average heat transfer coefficient of the hot fluid in the inner annulus is given by
av h
s av
h Q
A LMTD
Where the average log-mean temperature difference among the three fluid streams can be calculated as
2
hc hi
av
LMTD LMTD LMTD
The dimensionless performance parameters have been summarized as below. Nusselt number
hD
hNu k
Reynolds number
Re vD
h
Hydraulic diameter
4
h
D A
P
The Darcy friction factor for fully developed flowing a circular tube
2
2 pD
hf v L
2.5 Statistical Analysis and Objective of Work
A proper choice of design of experiments (DOE) is important for effective implementation of RSM. The matrix contains two factors with values on the Uncoded basis, Re with five levels and L/Dh with four levels, forming 20 runs. The corresponding responses (Nu and f), as predicted by CFD have also been presented in literature 19. Later, a central composite design (CCD) with the face-cantered approach has been applied to analyze with less number of data, without compromising the adequacy of prediction
CFD results of response variables are summarized in Tables 1 and 2. Further, a Response surface methodology has been applied to these results to get the optimum values. In the study
Presented in [19]
For determination of the optimum design parameters and interaction between them, data from numerical simulation or CFD modeling are used for optimization purpose in RSM. Because CFD modeling provides more accurate data with minimum error, reduces the experimental cost and save time compared to experimental run. So in the recent study, CFD is used to achieve
%degradation for optimization of heat transfer phenomenon in TTCHE.
Table 1 Design variables and levels of their values.
Coded values Design factors Symbol -1 0 1 Reynolds
number Re 250
0 6250 10,000 Length to
hydraulic diameter ratio
L/Dh 140 180 220
Table 2 Levels of design factors and CFD results of response variables.
Design factors
(Uncoded values) Response variables (Uncoded values) Run
Order Re L/Dh Nu F
1 2500 140 20.5885 0.0662134 2 2500 180 16.1273 0.0518672 3 2500 220 13.1995 0.0424368 4 6250 140 30.9013 0.047571 5 6250 180 24.2055 0.037264 6 6250 220 19.8372 0.0304887 7 10000 140 36.8984 0.0398602 8 10000 180 28.9031 0.0312238 9 10000 220 23.6792 0.0255468 2.6 Analysis of Variance (Anova):
The statistical significance is tested for those quadratic models by the ANOVA. The ANOVA results of the quadratic model of the f are listed in Table 3.
Table 3 Response Surface Regression: f versus Re, L/Dh Analysis of Variance Source D
F Seq SS Contr
ibuti on
Adj SS Adj
MS F- Val
ue P- Val
ue Model 5 0.0
012 56
99.87
% 0.0
012 56
0.0 002 51
46 4.8 8
0.0 00 Linear 2 0.0
011 88
94.41
% 0.0
011 88
0.0 005 94
10 98.
71 0.0 00 Re 1 0.0
006 80
54.08
% 0.0
006 80
0.0 006 80
12 58.
69 0.0 00 L/Dh 1 0.0
005 07
40.33
% 0.0
005 07
0.0 005 07
93 8.7 3
0.0 00 Square 2 0.0
000 46
3.68
% 0.0
000 46
0.0 000 23
42.
78 0.0 06 Re*R 1 0.0 3.10 0.0 0.0 72. 0.0
e 000
39 % 000
39 000
39 19 03 L/Dh
*L/Dh 1 0.0 000 07
0.57
% 0.0
000 07
0.0 000 07
13.
38 0.0 35 2-Way
Interacti on
1 0.0 000 22
1.78
% 0.0
000 22
0.0 000 22
41.
43 0.0 08 Re*L
/Dh 1 0.0
000 22
1.78
% 0.0
000 22
0.0 000 22
41.
43 0.0 08 Error 3 0.0
000 02
0.13
% 0.0
000 02
0.0 000 01
Total 8 0.0 012 58
100.0
0%
Model Summary
S R-sq R-sq
(adj) PRESS R-sq (pred) 0.000735
1 99.87
% 99.66% 0.00001
97 98.44%
The large value of the coefficient of multiple determination (R2=0.9987) implies that only 0.0009% of total variation cannot be reflected by the quadratic model. The large Values 1258.69 indicates the great significance of the regression model. The associate P-values less than 0.05 for the model indicate that the model terms are statistically significant and the effects of the model terms with the P-value greater than 0.05 are insignificant. In this case, it can be found in Statistically, F-test decides whether the parameters are significantly different. A larger F value shows the greater impact on the friction factor performance characteristics [15]. Larger F values are observed for Reynolds number (P=0.000) (54.08 %)
Table 3 shows the ANOVA result for friction factor. It is observed that the Reynolds number (P=0.000) (54.08 %) is most influences the friction factor followed by hydraulic diameter ratio (P= 0.000) (40.33%)
For both the models, "Pred R-Squared"
value is in reasonable agreement with the
"Adj R-Squared". It is predicted from the results of the ANOVA for TTCHE that the Reynolds number is the most dominating factor followed by hydraulic diameter ratio
Figure 4.1 Residual plots for friction factor
Figure 4.1 depicts the plots of residuals for friction factor respectively. As it can be observed from the normal probability plots in both the figures, the residuals are evenly distributed on both sides of the straight line indicating that the distribution of residuals for the friction factor are normal and thus, provide decent fit to the data.
Table 4 Response Surface Regression: Nu versus Re, L/Dh Analysis of Variance Source D
F Seq SS Contr
ibutio n
Adj SS Adj
MS F- Val ue
P- Val ue Model 5 445
.15 0
99.93
% 445
.15 0
89.
030 825 .22 0.0
00 Linear 2 428
.09 3
96.10
% 428
.09 3
214 .04 6
198 3.9 9
0.0 00 Re 1 260
.90 3
58.57
%
260 .90 3
260 .90 3
241 8.3 1
0.0 00 L/Dh 1 167
.18 9
37.53
% 167
.18 9
167 .18 9
154 9.6 7
0.0 00 Square 2 8.5
59 1.92% 8.5 59 4.2
80 39.
67 0.0 07 Re*Re 1 6.1
16 1.37% 6.1 16 6.1
16 56.
69 0.0 05 L/Dh*
L/Dh 1 2.4
44 0.55% 2.4 44 2.4
44 22.
65 0.0 18 2-Way
Interacti on
1 8.4
98 1.91% 8.4 98 8.4
98 78.
77 0.0 03 Re*L/
Dh 1 8.4
98 1.91% 8.4 98 8.4
98 78.
77 0.0 03 Error 3 0.3
24 0.07% 0.3 24 0.1
08 Total 8 445
.47 3
100.0
0%
Model Summary
S R-sq R-
sq(adj) PRESS R- sq(pred) 0.32846
1
99.93
%
99.81% 3.9296 6
99.12%
The large value of the coefficient of multiple determination (R2= 0.9993) implies that only 0.0007% of total variation cannot be reflected by the quadratic model. The large F value is 2418.31indicates the great significance of the regression model. The associate P-values less than 0.05 for the model indicate that the model terms are statistically significant and the effects of the model terms with the P-value greater than 0.05 are insignificant. In this case, it can be found in Statistically, F-test decides whether the parameters are significantly different. A larger F value shows the greater impact on the friction factor performance characteristics [15]. Larger F values are observed for Reynolds number (P=0.000) (58.57 %%)
Table 4 shows the ANOVA result for Nusselt no.. It is observed that the Reynolds number (P=0.000) (54.08 %) is most influences the friction factor followed by hydraulic diameter ratio (P= 0.000) (37.53%)
For both the models, "Pred R-Squared"
value is in reasonable agreement with the
"Adj R-Squared". It is predicted from the results of the ANOVA for TTCHE that the Reynolds number is the most dominating factor followed by hydraulic diameter ratio.
3 RESPONSE SUFACE METHOLOGY It's commonly used in the industry because it's the most effective technique for meeting welding requirements. This research looked at how to prepare low-cost goods and how to improve welding defects so that they work properly. This type of technique is commonly used to minimise costs and increase product quality, and it logs as functions of desired performance. Via rigorous design of experiments, the approach and variance in a process are minimised to aid in data interpretation and prediction of optimal outcomes. The following are the key RSM objectives and measures for the parameter design phase:
i. First, to set the objective for the overall experiment with the proper displacement.
ii. Output response will be identified with the proper measurements.
iii. Factors should be considered that affect the output response with the given levels and the interactions.
iv. The array should be set with the tests of experiments conducted on O.A.
v. To reduce the noise variance and the significance of process parameters full analysis for the sets of factors be formed with the defined array.
vi. Final set of optimal design parameters will be used to conduct the confirmatory experiments.
Fig. 3.1 Response surface methodology
Fig. 3.2 Response surface methodology 3.1 Confirmation test
Table 3.1 Multi-objective optimization results
Design
factors Leve l Opti
mal Level
Expe rime ntal
Predic ted (RSM)
Err or (%) NuNusselt
number A A2 36.8
984 36.931
6 0.0
332 Friction
factor B C1 0.03
9860 2
0.0397 0.0 001 The predicted value of the response variables is precisely closer to the numerical results and hence, it has helped
in reducing the size of the required data as the RSM provides useful interaction between the various parameters of the system.
4 CONCLUSION
Based on the results of numerical simulation and multi-objective optimization, the basic findings of this study have been summarized as follows.
1. From Figure 3 that the first Level provides maximum value of Nusselt number. (a) Reynolds number A1 2500 (b) Length to hydraulic diameter ratio), B2 180.
2. From Figure 3 that the first Level provides minimum value of pressure drop (friction factor) (a) Reynolds number A1 2500 (b) Length to hydraulic diameter ratio), B2 180.
3. Statistically, F-test decides whether the parameters are significantly different. A larger F value shows the greater impact on the friction factor performance characteristics [15].
Larger F values are observed for Reynolds number (P=0.000) (54.08 %) 4. Table 3 shows the ANOVA result for friction factor. It is observed that the Reynolds number (P=0.000) (54.08 %) is most influences the friction factor followed by hydraulic diameter ratio (P= 0.000) (40.33%).
5. Statistically, F-test decides whether the parameters are significantly different. A larger F value shows the greater impact on the friction factor performance characteristics [15].
Larger F values are observed for Reynolds number (P=0.000) (58.57
%%).
6. Table 4 shows the ANOVA result for Nusselt no.. It is observed that the Reynolds number (P=0.000) (54.08 %) is most influences the friction factor followed by hydraulic diameter ratio (P= 0.000) (37.53%).
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