Effect of Flow Structures on Heat Transfer in Single and Multiphase Jet

9428

Ind. Eng. Chem. Res. 2009, 48, 9428–9440

Effect of Flow Structures on Heat Transfer in Single and Multiphase Jet Reactors Sagar S. Deshpande,† Channamallikarjun S. Mathpati,†,‡ Sagar S. Gulawani,† Jyeshtharaj B. Joshi,*,† and V. Ravi Kumar*,‡,§ Department of Chemical Engineering, Institute of Chemical Technology, Mumbai - 400 019, India, and Chemical Engineering and Process DeVelopment DiVision, Center of Excellence in Scientific Computing (CoE-SC), National Chemical Laboratory, Pune-411 008, India

High frequency experimental measurements by hot film anemometry (HFA) of liquid velocities and temperature in the region of vapor-liquid (VL) and solid-liquid (SL) interfaces for two important reactor types, namely, condensation jet and jet loop reactors, have been studied for their heat transfer characteristics. An algorithm for flow structure identification has been devised from velocity data based on (i) zero crossings and (ii) continuous wavelet transform. The wavelet transform algorithm is especially found to be useful in accurately estimating both the age and size distributions of eddies near interfaces in a multiscale framework. Using these distributions, it is shown that the calculated values of heat transfer coefficients (HTC) at the SL and VL interfaces show remarkable correspondence with the HTC values obtained experimentally from instantaneous temperature measurements. For this purpose, a modified capacitance model has been proposed that takes into account the information about both the age and size distributions. The results obtained by the present methodology show the improvement possible for calculating the HTC at interfaces when compared with the earlier surface renewal models. It may therefore be used to study the interaction between flow dynamics and heat transfer behavior in chemical process equipment. 1. Introduction It is a pleasure to dedicate this festschrift paper to Dr. B. D. Kulkarni for his significant and extensive research and development contributions, spread over decades, that have brought the best of theory and practice together in chemical engineering to get the perfect blend. The present paper contibutes to this theme of amalgamating theory and practice by evolving new strategies that are based on a knowledge of the process performance and its sensitivity to operating ranges of parameters rather than empiricism. In order to reduce the empiricism, the importance of understanding transport phenomena from the point of finding existing relationships between the flow patterns and the design objective is needed. One way, this can be achieved is by using computational fluid dynamics to mathematically model the flow patterns and then use the information to calculate the hydrodynamic parameters such as pressure drop, hold-up, interfacial area, heat and mass transfer coefficients, etc. The other way is to devise advanced experimental techniques that capture accurately the phenomenological flow patterns in data sets which may then be used to complement model formulation and evaluation of the relevant hydrodynamic parameters. Using the latter approach, the present work aims to bring out a dependable methodology for the same from monitored data, and this is illustrated by applying it to two important reactor configurations exhibiting complex flows, namely, the single phase jet loop reactor (JLR) and multiphase condensation jet reactor (CJR). The JLR is widely used in industry for mixing purposes due to its convection-dominated flow.1-3 It has been used in applications for heat sensitive systems because of better mixing * To whom correspondence should be addressed. E-mail: jbj@ udct.org. Tel.: + 91-22-24140865. Fax: +91-22-24145614 (J.B.J.). E-mail: [email protected]. Tel.: +91-20-25902161. Fax: +9120-25902612 (V.R.K.). † Institute of Chemical Technology. ‡ Chemical Engineering and Process Development Division. § Center of Excellence in Scientific Computing (CoE-SC).

and heat distribution performance with the added advantage of being a simple cost-effective setup. The CJRs are used because of their very high heat transfer coefficient (HTC) values, (0.1-4.0 MW/(m2 K)) and are used in direct contact heat exchangers, cooling in nuclear engineering systems, refinery operations, etc.4,5 In both JLR and CJR, understanding the heat transfer characteristics is essential in order to increase the reliability of their design and obtain optimized performance. Therefore, in the present work, an attempt has been made to understand the relationship between the flow structures and heat transfer at the (a) vapor-liquid (VL) interface near the plume in CJR and (b) solid-liquid (SL) interface for conjugate heat transfer at the wall in both JLR and CJR. For this purpose, hot film anemometry (HFA) has been used because of advantages in simultaneously measuring both temperature and velocity at a given point with very high data acquisition rates (∼50 kHz). This enables accuracy in capturing features even near the smallest scales of turbulence. Herein, a new way is proposed for the improved prediction of HTC by eddy identification algorithms. The HTC behavior can be related to the flow characteristics obtained from the experimental velocity data for SL and VL interfaces provided the nature of the mechanisms operating at the interfaces are captured. Analysis of the data can provide the necessary means to infer these mechanisms because the distribution characteristics of the eddies in terms of age, size, and energy are embedded in it. Such an approach will then be generic and applicable to different categories of single and multiphase systems. 2. Previous Work The emphasis of previous work has been on developing empirical correlations that evaluate average HTC values. In the case of JLR, experimental measurements6,7 were carried out along the side wall of the reactor for analyzing the effects of various parameters, e.g., inlet velocity, nozzle diameter, and its inclination, on the average HTC. Computational fluid dynamics (CFD) simulations have shown the effects of mixing on

10.1021/ie900052s CCC: $40.75  2009 American Chemical Society Published on Web 05/20/2009

Ind. Eng. Chem. Res., Vol. 48, No. 21, 2009

temperature distribution and energy decays when hot fluid enters cold fluid in the reactor so as to avoid the formation of hot spots.8 However, the above simulation study was limited to the evaluation of average HTC and predictions of temperature profiles. The CJR has received more attention than JLR mainly because of its application in nuclear safety-related equipment where the phenomenon of direct contact condensation is involved. Much of the published work focuses on evaluating the plume dimensions, condensation flow regime maps, and temperature profiles in reactors for various geometric and operating conditions (nozzle diameter, nozzle upstream pressure, initial reactor temperature, reactor volume, etc). Semiempirical correlations4,9-17 have also been proposed for the calculation of average condensation HTC in the vicinity of plume (i.e., VL interface). The average HTC reported in literature is in the range of 0.1-4 MW/(m2 K). Experimental studies include measurements using holographic interferometry and high speed photography to find the plume shape and size. The average condensation HTC is then calculated by the knowledge of the heat flux and the plume interface area. Kim et al.15 estimated condensation HTC using three heuristic models, (i) interfacial transport (due to turbulent intensity), (ii) surface renewal, and (iii) shear stress. They found that the size of eddies at the steam-water interface plays an important role in determining HTC using the turbulent intensity model. The eddies were assumed to originate by steam condensation, and these then move away from the steam-water interface. The energy content of the eddies was proportional to the kinetic energy imposed on the steam-water interface. They used average interfacial stress and plume shape to estimate the turbulent shear velocity (u2,τ) at the VL interface. The surface renewal rate was then estimated from the correlation u2,τ2/Sυ ) 85 (from the work of Banerjee18). The mathematical formulation of the surface renewal model was improved upon by Kim et al.15 with a revised value of the constant in the above expression and evaluated by experiments. However, these heuristic models do not rigorously include the chacteristics of eddies and their movements near the interface that alter the heat and mass transfer characteristics. For this purpose, the effects of dynamics of the flow patterns as seen in the time series data needs to be appropriately included in the analysis for evaluating the HTC. 2.1. Theories of Heat and Mass Transfer. Heuristic models involve averaging the solutions of unsteady conduction equations with known boundary conditions, and they include the effects of turbulence close to the interface. Thus, they take into account the age distribution of structures at the interface. Various theories have been proposed to consider different aspects of turbulent structures close to interfaces, namely, their mean age, rate of surface renewal, and their age, size, shape, and energy content distributions. According to Lewis and Whitman,19 the bulk fluid is completely mixed and there exist free interfaces (in the form of a thin film), where only molecular motions are important for transport phenomena. Higbie20 proposed a different concept that free interfaces cannot dampen the effect of turbulence completely and that the eddies can reach up to the interface. Here, it was assumed that all eddies spend equal amount of time at the interface and then mix back with the bulk fluid. However, this assumption of equal contact time was found to be unrealistic. Danckwerts21 therefore extended the Higbie penetration theory by considering the random replacement of eddies at the interface and employed an exponential function for their age distribution. No experimental support was available for the presence of an exponential distribution which assumes that the maximum

9429

number of eddies have zero age at the surface. The above three theories predicted the dependency of HTC to thermal diffusivity (R) to the power of 0.5 or 1, whereas experimental observations showed it to be lying in the range of 0.5-0.8. This led to development of different models19-29 being proposed, viz., filmpenetration,22 surface rejuvenation,23 random surface renewal,24,25 large eddy,26 small eddy,27,28 and damped turbulence.29 Fortuin and co-workers24,25 carried out laser Doppler velocimetry (LDV) measurements close to pipe wall and, using the conditional sampling criteria of Blackwelder and Kaplan,30 found that the age distribution is exponential, i.e., a maximum number of eddies were having life close to zero thereby supporting Danckwert’s theory. Fortescue and Pearson26 visualized the flow near the interface as a regular sequence of steady square roll cells touching the interface. They assumed that the convective effects of the turbulence on the flow field near the interface can be accounted for by assuming that large eddies continuously renew the interface and take part in the heat/mass transfer process. The model required the knowledge of turbulence characteristics (u2,rms and lI) of large eddies in the bulk. This large eddy model assumes that the interfacial forces are dominated by large eddies as compared to the motion of the smaller eddies which are swept at the interface. The theory therefore asumes that the smaller eddies have negligible contribution to the heat/mass transfer. On the other hand, Banerjee et al.27 and Lamont and Scott28 proposed that the small eddies control the transport phenomena at the interface. Although, the large eddies have larger residence time at the interface, it was assumed that the small eddies have more mobility. Thus smaller eddies contribute more to the interfacial turbulence and promote mixing at the interface. This small eddy model showed enhanced HTC values by incoporating two parameters, namely, kinematic viscosity (υ) and the rate of energy dissipation per unit mass (ε) following Kolmogorov’s hypothesis. Although the large eddy and the small eddy models were used to estimate the HTC, the results were applicable only to the specific systems studied and thus not generic. A single eddy model31 showed that the integral length scale may not be a true representative of the eddy size distribution and the use of an average of length scale distribution was suggested. Also, instead of using root-mean squared (rms) velocity in the bulk, the use of an average characteristic velocity for eddies was proposed. Theofaneous et al.32 studied the gas absorption by a turbulent liquid in the absence of external interfacial shear. They identified two distinct heat transfer regimes associated with energy containing and energy dissipating turbulent motion and obtained a relationship for each regime based on the turbulence Reynolds number (Ret). According to this study, for Ret . 1 the mass transfer coefficient is controlled by the small scale motion, while for Ret , 1 the mass transfer coefficient is controlled by large scale motion. Thus, the earlier studies show that the effect of flow behavior needs to appropriately account for eddy age distribution. Also, this accounting needs to be more generalized and applicable to extreme situations (e.g., stagnant/ moving, vapor-liquid (VL) and solid-liquid (SL) interfaces) for varying operating conditions. There exists a need for new methodologies that address these concerns, and this, therefore, has provided the motivation for the present work. In the above context, applications of wavelet transform (WT) and multiresolution analysis (MRA) to reaction engineering systems from the point of process monitoring,33-35 noise reduction,36-38 fault detection,39,40 and turbulence analysis41-46

9430


have found increasing attention in recent years. In particular, for turbulent systems, WT analysis is advantageous because it studies the energy decomposition of nonstationary flows in a localized way. This it does by convolution of data with suitable wavelet basis kernel functions that have finite energy with welldefined properties. The wavelet coefficients obtained by the WT systematically span different time and frequency scales of the flow and provide the capability to study multiscale phenomena.47 Thus, convolution of wavelet functions with data have been used to identify and resolve different types of structures that are simultaneously present in the flow dynamics46 and its applicability is shown for important classes of chemical process equipment. In particular, the continuous wavelet transform (CWT) approach may be used to study the evolution and interaction of structures dynamically and at different scales. This may be carried out by using the wavelet transform modulus maxima (WTMM) methodology.41-43 The WTMM may be used to evaluate the age and size distributions of the flow structures especially near the VL and SL interfaces as is addressed in the present work. It may then be useful to incorporate this additional information in appropriate formulations for improving accuracy in calculating the HTC values. In the next section, the description regarding the experimental techniques and conditions employed to collect the data is presented. Section 4 develops eddy identification methodology (EIM) formalisms used for studying flow structure behavior and discusses the relative merits of analyzing the velocity/temperature data either by zero crossings or by the more rigorous CWT based multiresolution analysis. For the available experimental data, the HTC values obtained using classical concepts and using the present model based on age and size distribution of eddies are compared in section 5. The results show the applicability and advantages of EIM in studying HTC behavior. 3. Experimental Techniques The JLR was made up of a cylindrical plexiglass tank of 0.3 m internal diameter and 0.4 m height. The liquid was circulated using an external 0.5 HP centrifugal pump. The nozzle position was fixed at HN/D ) 1 with downward orientation as shown in Figure 1. The HFA measurements were carried out along the SL interface at different axial locations (0.07-0.35 m) 5 mm away from the wall. Figure 2A shows the schematic of the experimental CJR setup. The meaurement locations in CJR are shown in Figure 2B. CJR consists of a boiler, rectangular tank, a nozzle of 1 mm internal diameter, and finger type heat transfer surface. The boiler with a capacity of 5 kg/h with a pressure up to 0.35 MPa was used. A rectangular plexiglass tank had internal dimensions of 0.4 m × 0.4 m × 0.7 m with a wall thickness of 0.012 m. The submergence of nozzle was 0.05 m from the bottom. A finger type, rectangular box of 0.05 m × 0.3 m × 0.5 m with a wall thickness of 0.002 m (SS-316) formed the additional heat transfer surface. The measurements were carried out at different axial locations (0.005-0.05 m) at the VL interface and (0.08-0.35 m) at the SL interface (Figure 2). The HFA is based on convective heat transfer from a heated wire or film element placed in a fluid flow. Any change in the fluid flow condition that affects the heat transfer from the heated element will be detected virtually instantaneously by a constant temperature anemometer (CTA)/constant current anemometer (CCA) HFA system. The HFA can therefore be used to provide information about the velocity patterns and temperature at a

Figure 1. Schematic of the JLR showing the flow pattern and the HFA probe near the wall.

measurement location. The electrical power input is equal to the power lost to convective heat transfer,48,49 I2Rfilm ) hAfilm(Tfilm - TB)

(1)

where h is the heat transfer coefficient, I is the supplied input current, Rfilm is the resistance of the film, Afilm is the area of film, Tfilm is measured temperature at the film, and TB is the surrounding temperature of the bulk fluid. The HFA (Dantec make) has been used for the measurement of local flow velocity and temperature. Dual sensor of X-Film type (quartz fiber probe 55R61 covered by Ni thin film of thickness 0.1 m, sensor diameter 70 µm, overall fiber length 3 mm, sensor length 1.25 mm) has been used for simultaneous measurement of two components of velocity, namely streamwise and wall normal. The CTA module was used to record velocity while the CCA module was used to measure the temperature. Using the CTA module with X-film probe, two components of velocity were measured simultaneously. For the simulatneous measurement of velocity and temperature (CCA module), one film from the probe was connected to record velocity and other for temperature. A two-dimensional (2D) traverse with precision of 0.5 mm has been used for movement of the probe in the longitudinal and transverse directions. In the present study, data sets of 2.2 million points each were collected at a frequency of 20 kHz at each reactor location. 4. Eddy Identification Methodologies (EIM) Two algorithms for EIM, one based on zero crossings of velocity/temperature and the other based on CWT, for identification and isolation of eddies have been employed in this study. The discussion below brings out the principles of the individual methods and their relative merits. 4.1. Eddy Identification Method Based on Zero Crossings (EIM-ZC). For the identification of eddies, Luk and Lee31 developed an approach based on zero crossings in fluctuating velocity component. As an eddy passes through the measurement point, the velocity fluctuates about its mean value (Figure 3A). Subtracting the mean value, we obtain the fluctuating component of the velocity. As seen in Figure 3B, which represents a small window of the data in Figure 3A, the fluctuating component


9431

Figure 2. (A) Schematic of CJR showing the plume (VL interface) and the cooling finger type heat exchanger: (CW) cooling water. The HFA probe connected to the CTA module and is used for measurements either at the SL or VL interface: (1) tank; (2) nozzle. (B) Measurement locations in CJR.

eddy identification. Thus, from a plot of fluctuating velocity (u2′) versus time, as the velocity vector crosses the time axis, the life of one eddy may be considered to end while another one begins. Alternatively stated, it may be proposed that the time gap (∆t) between two successive crossings represents one eddy. Different eddies show unequal time gaps (∆t1, ∆t2,..., ∆tn) as shown in Figure 3B, and these gaps are taken as the life of respective eddies. The characteristic energy of an eddy may be obtained by squaring and summing the fluctuating components within an identified eddy27,29 as

∑ 21 u′

2 2

kE,i )

i

(2)

∑ i

The characteristic eddy velocity for ith eddy was then estimated by uE,i ) √2kE,i

Figure 3. Description of EIM-ZC. (A) Sample velocity time series from HFA. (B) Magnified window region of part A showing the zero crossings in the fluctuating velocity. Eddy ages are indicated by ∆t1, ∆t2, etc.

has both positive and negative values and therefore it crosses the time axis at many locations. Within consecutive zero crossings of the fluctuating component, the fluid elements in the measurement location would therefore have similar kinetic properties, and this may be considered to be the criterion for

(3)

The eddy length scale (lE) was calculated from the eddy lifetime (∆tE) and the characteristic eddy velocity (uE). All eddies were sorted according to their age. The age distribution function (φ(t)) was then estimated and identified the fraction of eddies having life between t and t + ∆t. 4.2. Eddy Identification Method Based on Continuous Wavelet Transform (EIM-CWT). In the case of CWT, an appropriate wavelet basis function ψ is chosen to convolve the 1D data u2(t) into time-scale components by means of translations b and dilations a of ψ as given by Ta,b i )

∫ u (t)ψ

a,b

2

(t) dt

(4)

9432


Figure 4. Description of EIM-CWT. (A) Sample velocity time series from HFA. (B) CWT scalogram of the fluctuating velocity component bringing out the eddy characteristics in time and WT scales. (C) WTMM maxima lines with systematic identification of the start time of eddy formation (+), its end time (*), and eddy age (T).

The wavelet function ψ may be selected as the nth derivative of a Gaussian (DoG) function because of its advantage in computing higher order derivatives while still maintaining the compactness and scalability of the wavelet basis function,50,51 i.e., ψ(n)(t) ≡

dn -(1/2)t2 e dtn

(5)

Using the Gaussian function, the deterministic trends up to (n - 1)th order may be eliminated by a local polynomial fit and then studying the residual for its multifractal properties and for extracting the masked singularities. The identified singularities relate to the presence of distinct structures in the flow.41,42 Further, by the methodology of wavelet transform modulus maxima (WTMM), only the local maxima of |Tia,b| (eq 4) are chosen and grouped to obtain the loci of maxima as a function of t across the scales a.51 The observed maxima lines delineate structures and their passage in the multiscale WT domain. More precisely, when the WTMM is applied to the data captured near the VL and/or SL interfaces, these analyses bring out the passage of eddies in time and therefore their effects on the surface renewal phenomena may be analyzed. A proper implementation of the WTMM and scanning the modulus maxima lines systematically across wavelet scales may be used to obtain properties including the start time of eddy formation, its end time, eddy age distribution, eddy energy and their distribution, and eddy break-up and energy transfer mechanism across the WT scales. Figure 4 shows typical results of a study by WTMM and analyzing the maxima lines for eddy identifica-

tion and their properties. Eddy identifcation was carried out by coding in MATLAB by analyzing for array oriented data constructs on the maxima lines. 4.3. Relative Merits of EIM-ZC and EIM-CWT. The main advantage of EIM-ZC is that it is possible to evaluate the eddy age distribution φ(t) in a simple way. Although, CWT requires increased computational time, it is more rigorous because eddies have been isolated on the basis of detection of singularities. The EIM-ZC shows the presence of large number of small eddies when noise is present in the data. This may lead to interpretations deviating from reality. The situation may be improved by denoising the data by suitable techniques.36,46 In the present study, we employ a procedure using discrete wavelet transform and as described in the work of Roy et al.36 For EIMCWT, because the basis function has been dilated and translated over the range of scales, the frequency separation is in situ. It identifies eddies according to frequency scales and a separation of eddies at all scales is observed. The EIM-CWT offers the advantage of studying eddy behavior at desired scales, and the effects of noise are naturally diminished. 5. Results and Discussions All the classical theories work well for the experimental conditions under which they were developed, but it is observed that they deviate significantly for different operating conditions. This may arise due to the fact that the effects of the existing flow patterns have not been adequately considered. Therefore, an attempt has been made to estimate the actual age distribution function from monitored data at two extreme interfaces (SL and


Figure 5. Flowchart summarizing the algorithm and the steps involved in evaluation of HTC using theoretical models, EIM-ZC and EIM-CWT based modified capacitance model, and experimental data. Table 1. Age Distribution Functions investigator

age distribution function

20

Higbie

φ(t) )

Danckwerts21 Perlmutter52 Fortuin et al.25

{

1/tc 0 < t < tc t > tc 0

tc is mean contact time φ(t) ) S exp(-St) S is surface renewal rate tanks-in-series model φ(t) ) {(mmtcm-1)/[(m - 1)!tcm] exp(-mt/tc) m ) no. of tanks in series φ(t) dt ) e- t/tc d(t/tc) tc is mean contact time

VL) using EIM-ZC and EIM-CWT methodologies. Here, we propose a new model that is based not only on the sensitivity of age distribution but also on the size distribution for calculation of HTC. A flowchart summarizing the algorithm and the steps involved in evaluation of HTC is presented in Figure 5. The results so obtained are compared with results of heuristic models (Tables 1 and 2). 5.1. Eddy Age Distribution. Figure 6 shows the age distributions from various theories (Table 1) along with that obtained by EIM-ZC and EIM-CWT at the VL interface in CJR. The simplest age distribution function of Higbie20 considers constant contact time of eddies at the interface and is therefore represented as a step function in Figure 6 (line 1). Danckwerts21

9433

discarded the concept of constant contact time and proposed a surface renewal rate as a reciprocal of mean eddy age. This is reflected by the exponentially decaying age distribution function (Figure 6, line 2). However, it predicts that the most probable age of fluid elements at the wall is zero. The Higbie and Danckwerts distributions may be identified as the residence time distribution (RTD) function of plug flow and well-mixed systems, respectively. Perlmutter52 suggested that the correct distribution function should lie somewhere in between these two. Therefore a distribution function for a system of m well-mixed vessels in series was proposed. The special case of m ) 1, reduces to the Danckwerts distribution while m f ∞ gives the Higbie distribution. Perlmutter52 suggested that there is a zero likelyhood of finding an eddy with zero residence time and the most probable age for two tanks in series is [τ1τ2/(τ1 - τ2)]ln (τ2/τ1) (Figure 6, lines 3-5). Imperfect mixing of the interfacial fluid using the concept of dead time was also considered. The presence of stagnant (i.e., unreplaced) fluid elements led to a delayed exponential distribution (Figure 6, line 6). For the first time, Fortuin et al.25 evaluated the age distribution using LDV velocity data (Figure 6, line 7). However, the empiricism was introduced by the conditional sampling technique through a manipulation of threshold levels. Also, the technique was specifically developed for the SL interfaces and may not be applied to the VL and LL interfaces because distinct sampling criteria for eddy identification are not available for these cases. If turbulence is considered as a purely random process, the ideal age distribution would be Gaussian. Depending on the flow dynamics the turbulence can also contain structures that introduce skewness in the distribution. Therefore, it is desirable to have a universal technique that is applicable to all types of interfaces (SL, VL, and LL) and accounting for the effects of eddy age distribution. In the above context, results of carrying out analysis with EIM-CWT and EIM-ZC using HFA measurements show the technique to have potential for applying to various types of interface and the results obtained are discussed below. The HFA has the advantage of obtaining data at an high acquisition rate with equal time spacing. The high data acquisition rate provides very good frequency resolution and is essential in order to capture the eddies until the dissipation range and avoids biased views arising because of the low data rate. Low data rate sampling may not show the contribution of very small age eddies and the distribution will always be exponential, while in reality it may be skewed. Eddy ages obtained from the acquired time series data by EIM-ZC and EIM-CWT, respectively, were therefore used to obtain the actual age distribution functions. This is different from the models presented in Table 1 which assume the mathematically defined distribution functions. The EIM-ZC and EIM-CWT evaluate the age distribution functions based on the identified singularities in the data. Figure 7 shows the age distribution obtained for the VL and SL interfaces in the CJR. The distribution at the SL interface is found to be narrower as compared to the VL interface. Also, the mean age (tc) is found to be 2.63 and 0.031 s, for SL and VL interfaces, respectively. Thus, for the VL interface, we clearly see a 2-3 lower order of magnitude in the mean age value as compared with that obtained at the SL interface. Another interesting observation can then be inferred from Figures 6 and 7. For VL interface, the tanks in series model with m ) 2 is seen to be close to the age distribution results obtained by EIM. On the other hand, at the SL interface, the model with m ) 5 gives better agreement. Because the corresponding age distribution suggests a decrease in the number

9434


Table 2. Heat Transfer Theories author 19

theory

Lewis-Whitman Higbie20 Danckwerts21

film theory penetration theory surface renewal

Fortescue-Pearson26

large eddy

Banerjee et al.27 and Lamont and Scott28

small eddy

Luk and Lee31

single eddy

of tanks required, it may be concluded that, for the situations where small eddies dominate, the age distribution function shifts toward lower m, i.e., for higher surface renewal rates. These results therefore indicate that flow structure classifications can be made using the age distribution functions.

heat transfer coefficient hj ) R/δ hj ) 2FCp[R/(πtc)]1/2 hj ) FCp(RS) hj ) 1.46FCp[Ru2,rms/lI]0.5 where 2 R(τ) ) 〈u2′(t)u′(t 2 + τ)〉/〈u2′ 〉 tI ) ∫t* R(τ) dτ 0 t* is the time when the autocorrelation function first become zero lI ) u2,RSMtI hj ) 0.4FCp[R/(V/ε)0.5]1/2 where ε ) 1/NE∑NE uE3/lE hj ) 0.9FCp[R/(lj/ujE)]1/2 where NE NE jl ) (1/NE)∑i)1 li, ujE ) (1/NE)∑i)1 uE,i

5.2. Heat Transfer Coefficient (HTC). The evaluation of HTC has been carried out using various models as shown in Table 2. The theories of Higbie and Danckwerts are based on a single parameter that defines the eddy age distribution for calculation of the HTC. On the other hand, as seen in Table 2, for the small, large, and single eddy models while using the basic formulation of Higbie, other parameters such as the mean contact time from integral length, velocity and time scales, dissipation rate, etc. are needed for the calculation of HTC. It may be noted that in these approaches the influence of distribution of eddy age has not been considered. 5.2.1. Limitations of Single Parameter Theories. To study the sensitivity of HTC calculations, we thus chose to study and compare the properties of the two extreme age distributions used in Higbie and Danckwerts models. The HTC expressions for these theories are as follows: Higbie20 theory hH ) 2FCP

R πtc

(6)

Danckwerts21 theory hD ) FCP√RS ) FCP Figure 6. Comparison of eddy age distribution functions for CJR near VL interface (line 1, Higbie model; line 2, Danckwerts model; line 3, Perlmutter tanks-in-series model (m ) 2); line 4, Perlmutter tanks-in-series model (m ) 4); line 5, Perlmutter tanks-in-series model (m ) 6); line 6, Perlmutter delayed exponential model; line 7, Fortuin et al.; O, EIM-ZC; *, EIMCWT).

R tc

(7)

It is interesting to note the percentage change in prediction of HTC evaluated from these two theories as

hH - hD × 100 ) hD

( ) ( ) 2FCP

R - FCP πtc

FCP

(

R tc

R tc

)

× 100 )

2 - 1 × 100 ) 13% √π

(8)

Equation 8 suggests that for either age distributions, the predictions can vary only within 13% of the mean age. Thus, it is clear that the age distribution cannot be the sole parameter that governs the heat and mass transfer behavior at the interfaces. Therefore, in the present study, we propose a new modified capacitance model that may be used to calculate HTC values. 5.2.2. Modified Capacitance Model. Here we propose that the size distribution of flow structures is an important parameter that needs to be taken into account to calculate HTC values. Consider three different flow structures E1, E2, and E3 as shown in Figure 8 with Figure 7. Comparison of eddy age distribution functions using EIM-CWT for CJR (O, VL interface; 0, SL interface).

tE,1 ) tE,3 ) (1/2)tE,2

(9)


kE,i )

∫

tE,i

tE,i

u2′2 dt

(10)

( )

T(x1,t) ) (TS - TB)erf

x1

+ TS

√4Rt

9435

(12)

with the heat flux at the interface given by kE,1 ) kE,2 ) (1/2)kE,3

(11) ∂T ∂x1

q)K where kE,i gives the energy content of the ith eddy. Heuristic theories that consider only the respective eddy ages (i.e., effect of tE1, tE2, and tE3) will predict that the contribution of flow structures E1 and E3 are same because the passage times are equal. In comparison the contribution of E2 will be 1/2 times that of E1 (from eq 6). The equal contributions of E1 and E3 arise because the basic derivation follows the unsteady heat diffusion in an infinite medium. At t ) 0, the rate of transfer will be highest and this rate will reduce with time due to the development of a temperature profile near the interface. When we consider the characteristics of E1 and E3, then mixing by E1 is more vigorous than by E3. However, for the equal passage times when the mixing in E1 is more vigorous than E3, it implies that the size (lE,1) of eddy E1 is greater than than the size (lE,3) of eddy E3. Thus, more area is available for the eddy E1, and this increases the heat transfer. Otherwise stated, the higher energy content of E1 will make the temperature uniform in a reduced time when compared to E3 while keeping the gradient for heat transfer higher. Therefore, the heat transfer in E1 will take place at a rate much closer to the initial rate within the prescribed contact time of E1. Similar arguments can be made while comparing the contributions of structures E2 and E3. When we compare E2 and E3 based on eddy age (tE2 > tE3), ths heat transfer conribution of E2 is significantly lower that of than E3 (eq 6). However, because of the higher energy of E2 as compared to E3, the resulting l2 will be larger than that of the l3 and the area available for the heat transfer will be lesser for E3. Thus, when eddy age and resultant size (area) distributions are taken collectively, the HTC for E2 may surpass that of E3. These aspects have not been addressed in the models presented in Tables 1 and 2 and may lead to the observed large deviations in the predictions of HTC from experimental values. A modified capacitance model that uses Perlmutter’s tank in series model52 to account for the effects of the size of the flow structures is discussed next. 1. The equation for temperature profile is the solution of the unsteady heat diffusion equation24

Figure 8. Hypothetical situation for illustrating the effects of eddy age, size, and energy on heat transfer characteristics. (A) Fluctuating velocity time series showing three types of eddies E1, E2, and E3 with ages t1, t2, and t3, respectively. (B) Kinetic energy of eddies E1, E2, and E3.

|

(13)

x1)0

for constant temperature boundary conditions. From the properties of the error function (eq 12), we have the heat flux q given by24

[ ( )]

q ) K(TS - TB)

x12 2 exp 4Rt √π

2

x1)0 √4Rt

(14)

2. The time averaged heat flux qj may be used to evaluate the HTC as h)

qj (TS - TB)

(15)

where, in classical theories of heat and mass transfer, qj is evaluated as

∫ qφ(t) dt ∫ φ(t) dt ∞

qj )

0

(16)

∞

0

Here, φ(t) is the age distribution function and the integral in the denominator over 0 to ∞ is used to normalize. 3. A new formulation is proposed for the evaluation of qj which takes into account the combined effects of age and size distributions. Figure 9A and B shows the eddy size distributions using EIM-CWT for three different eddy ages for CJR at VL and SL interfaces, respectively. The study of distribution functions obtained from EIM-CWT shows that for the flow structures of same age there is a wide distribution of eddy size and the energy content. The combined effect of eddy age and size can be estimated as

∫ qφ(t)( ∫ φ(t,A ) dA ) dt ∫ φ(t)( ∫ φ(t,A ) dA ) dt ∞

qj )

0

∞

0

∞

0 ∞

0

E

E

E

(17)

E

where φ is the function corresponding to the area scale distribution obtained from the eddy energy (kE) and the eddy life (tE). Here, AE represents area of the eddy which is of O(lE2). The EIM-CWT methodology offers a way to calculate both the eddy age φ(t) and area φ(t,AE) distributions. Equation 17 is used for evaluting the average heat flux (qj). The size distributions are normalized with respect to the mode of area (i.e., most frequent value). The resulting area distributions therefore varies around unity. Its effect on (qj) will be negligible only when the distribution is a delta function at 1. The degree of spread around unity suggests the presence of a broader distribution of multiple size eddies. At the VL interface, the size distribution is found to be wide for small eddy ages i.e., 0.003 and 0.02 s (Figure 9A, lines 1 and 2, respectively), while for large age eddies (0.5 s), it is narrower (Figure 9A, line 3). This suggests that larger age eddies contribute to a lesser extent in affecting the HTC. On the other hand, the eddies with a broader size distribution can enhance the HTC value, which is clearly observed at the VL interface. On the other hand, at the SL interface, the distribution shows variation in narrow bands at small ages, i.e.,

9436


Figure 10. Normalized distribution of instantaneous hexp evaluated from HFA temperature measurements showing a wide variation in CJR. (A) VL interface. (B) SL interface. Figure 9. Normalized size distribution function based on area AE [of O(l2)] of flow structures and obtained by EIM-CWT for CJR. (A) VL interface (line 1, ∆t ) 0.003 s; line 2, ∆t ) 0.02 s; line 3, ∆t ) 0.5 s). (B) SL interface (line 1, ∆t ) 0.1 s; line 2, ∆t ) 2 s; line 3, ∆t ) 7 s).

at 0.1 s (Figure 9B, line 1). It becomes wider for ages near the peak of the eddy age distribution (Figure 9B, line 2 for t ) 2 s) and again narrows down toward the larger ages (Figure 9C, line 3 for t ) 7 s). At the SL interface, the area distribution is seen to be narrower compared to the VL interface, and also, it is skewed toward smaller size eddies. This results in a small reduction in the HTC. 5.2.3. Experimental Heat Transfer Coefficient. Instantaneous temperature for calculating the HTC was obtained using CCA module of HFA. The CCA module works on the principle of convective cooling of the probe. On the basis of instantaneous temperature close to probe, there is a change in voltage of the probe. The bulk temperature was monitored and was found to be constant for the measurement duration. Since input current is known in CCA module of HFA, the amount of energy supplied to the probe is known. The bulk temperature was measured by thermocouples. For the specified surface area of the probe (Afilm) exposed to the flow the HTC (i.e., hexp) can be obtained from eq 1 as hexp )

I2Rfilm Afilm(Tfilm - Tf)

(18)

The hexp obtained using this procedure has been plotted in Figure 10 as a histogram. It can be observed that the instantaneous hexp varies by three to 4 orders of magnitude. The observation of a wide distribution of hexp brings out the necessity for considering flow behavior close to the probe when taking measurements near the VL and SL interfaces.

5.2.4. Comparison of HTC. The instantaneous hexp obtained experimentally have been averaged to get hjexp and are compared with the predicted hj in Figure 11A-C for different axial locations at SL and VL interface in the CJR and the JLR using EIM-ZC and EIM-CWT along with the modified capacitance model (eqs 15 and 17). The predictions are in very good agreement with the experimental values at SL interface, with better predictions in general by EIM-CWT. Figure 11A shows that HTC at VL interface goes through a maximum at 0.015 m above the nozzle inlet and average HTC (hj) ranges between 0.1 and 4 MW/(m2 K). The reason for the peak is that closer to the nozzle inlet (x2 < 0.015 m), the steam jet void fraction is greater than 0.995. However, for x2 ≈ 0.015 m, the surrounding water also evaporates and this results in a even higher HTC value. At very close to plume, the turbulent intensities are found to be very high (approximately 12-15%). The intensity then decreases as one moves away from the plume and hj values fall. Also, flow velocities in the bottom section (x2 < 0.015 m) close to VL interface is seen to be more turbulent than in the top section (x2 > 0.015 m). Figure 11B shows the hj variation at SL interface for CJR at finger wall. It is observed that hj increases in this case from bottom to top. This is because the finger top side experiences higher liquid circulation velocities compared to the bottom. The hj varies within a range of 360-830 W/(m2 K). In JLR, a similar trend is observed for hj as that for finger wall in CJR. The hj was found to decrease with decrease in liquid circulation velocity from reactor bottom to top. Two circulation loops are formed in the reactor, and therefore, near the wall almost unidirectional flow is observed. The hj obtained are seen to be higher compared to that in CJR at finger wall. This is because most of the input energy of liquid jet is utilized to


9437

Figure 12. Parity plot at VL interface for CJR between the hjexp and predicted hj using EIM-CWT (9); EIM-ZC (2); small eddy model (0); large eddy model (∆); surface renewal model (×); and Higbie model (]).

Figure 11. Comparison of hj using EIM-ZC and EIM-CWT and hjexp along axial locations (x2) in the reactor. (A) VL interface for CJR. (B) SL interface for CJR. (C) SL interface for JLR (hjexp values ([); EIM-CWT based hj (9); EIM-ZC based hj (2)).

develop convective flow. The hj is found to be proportional to local liquid velocity to the power 0.6-0.7. 5.2.4.1. Heat Transfer at the VL Interface. The values of hjexp have been further compared with the calculated hj from the models presented in Tables 1 and 2, and the results are shown for VL and SL interfaces as parity plots in Figures 12 and 13. In CJR, at VL interface hjexp are observed in a range of 0.1-4 MW/(m2 K). All the theories have been compared on the basis of effective exposure time. This exposure time is defined as (tc) for Higbie,20 (1/S) for Danckwerts,21 (lj/ujE) for single eddy,31 (lI/u2,rms) for large eddy26 and ([ν/ε]1/2) for small eddy27,28 models (see Tables 1 and 2). Using the experimentally monitored velocity values (u2), the exposure time and hj for the above models have been calculated (with the formulas presented in Tables 1 and 2). In all the theories, the constant of proportionality is nearly equal to 1 (see Table 2). Therefore, the hj predictions are very sensitive to calculated values of the effective exposure time of eddies. Figure 12 clearly shows that Higbie and Danckwerts theories deviate significantly from experimental values because the skewness of age distributions, toward small eddies at VL interface, is not included in their formulation. The most frequently encountered exposure time is observed to be 0.018 s, whereas the mean exposure time is 0.031 s at (x1, x2) ) (0.005 m, 0.03 m). The small eddy and large eddy models

Figure 13. Parity plot at SL interface for CJR between the hjexp and predicted hj using EIM-CWT (9); EIM-ZC (2); small eddy model (0); large eddy model (∆); surface renewal model (×); and Higbie model (]).

have different considerations regarding the size group of eddies controlling the heat transfer at the interface. The large eddy model was specifically developed for open channel flows where major turbulence generation is away from the wall. Therefore, the large eddies from the bulk come closer to the interface and renew the surface without significant break-up into small eddies. So in this formulation, the integral length scale and rms velocity of the bulk are considered. The small eddy model was developed for flows such as falling films, bubble transport through pipelines, etc. This model considered the contribution of small eddies at the interface by considering the dissipation rate at the interface without going into more details of their formation. The dissipation rate was estimated from the bulk turbulence energy spectrum. In the present study, at (x1, x2) ) (0.005 m, 0.03 m), the effective exposure time for the small eddy model (≈0.006 s) is much smaller than that for the large eddy model (≈0.0135 s). However, all previous theories could not consider the combined effect of exposure time and total surface area of individual eddies at the interface. This effect has been taken into account by modified capacitance model and the model parameters such

9438


as eddy size and age distributions have been estimated using EIM-ZC and EIM-CWT methodology. The area wighted effective exposure time is found to be 0.0023 s using EIM-ZC and 0.00192 s by EIM-CWT. 5.3.4.2. Heat Transfer at SL Interface. Similar results are observed in the case of SL interface as shown in Figure 13. At SL interface, hjexp is observed in the range of 200-1300 W/(m2 K). The flow structures developed at SL interface are mainly governed by the generation of turbulence at the wall as well as turbulence convected from the bulk by large eddies. The contribution of latter is found to be significant as compared to the first. Therefore, the flow structures at the interface can be characterized by the exposure time estimated from bulk turbulence parameters. At the SL interface, the surface renewal and Higbie models are found to considerably deviate from the hjexp values. Due to narrow age distribution, the most frequently observed exposure time (≈2.2 s) is seen to be very close to the average exposure time (≈2.31 s). The large eddy model is observed to be in good agreement with the hjexp with slight overprediction, and this can be readily explained by length scale distribution as shown in Figure 9. Unlike the VL interface, large length scale eddies are higher in number at the SL interface. Hence, the effective exposure time (1.15 s) based on the integral length scale and rms velocity is found to be less than that of the Higbie model. The small eddy model underpredicts by 60% from the experimental values of hjexp. This may be because the small eddy model considers the Kolomogorov length scale as the controlling size group, and in this range [O(10-6 m)], it is not possible to monitor by HFA. This is reflected in terms of the lower value of effective exposure time of 1.83 s. In the case of EIM-ZC and EIM-CWT based on modified capacitance model, the length scale distribution shows a very narrow distribution for smaller ages, while the distribution is broadened for larger ones and becomes significant for ages close to mean exposure time. In this way, the area based corrections for the large age elements result in a net reduction of hj. Therefore, the hj based on the modified capacitance model is seen to be lower than that obtained from the large eddy model but lying close to the experimental values of hjexp. Also, the EIM-CWT and EIMZC show effective exposure time of 1.26 and 1.34 s, respectively, and hence, the EIM-CWT shows higher values of hj than EIM-ZC, making it more accurate. In all the cases, the predictions of EIM-CWT and EIM-ZC studies have shown significant improvements when compared to the existing theories because the modified phenomena of size as well as age distribution is considered. Thus, it can be concluded that correct evaluation of distribution functions is of prime importance to study the transport phenomena at the interfaces. 7. Conclusions Here, we show the importance of analyzing and incorporating the role of structures present in the flow for evaluating heat transfer characteristics at vapor-liquid and solid-liquid interfaces for two reactors with turbulent hydrodynamics, namely, condensation jet and jet loop reactors using data obtained by hot film anemometry. The paper provides an experimental demonstration of the role of turbulence in heat transfer calculations. The analysis has shown that it is possible to obtain heat transfer coefficients accurately at the wall and plume interfaces of these reactors. The HFA data is seen to capture the basic process phenomenology because of its advantages in sampling data at high frequencies. Using the velocity data monitored in the region of the VL and SL interfaces along with eddy

identification methodologies, namely, EIM-ZC and EIM-CWT, it is shown that the eddy age and size distributions can be accurately characterized. These distributions calculated from experimental velocity data considerably improve the predictions of HTC and the predicted HTC show good agreement with hjexp obtained directly using temperature measurements by HFA. The present study shows the considerable potential of using continuous wavelet transforms along with wavelet transform modulus maxima methodology to accurately resolve and characterize flow structures at interfaces in a multiresolution framework. The algorithms presented here for EIM are generic and likely to be applicable to study interfacial phenomena for other types of reactors with complex flows. The availability of flow structure distrubtions is particularly advantageous because classical surface renewal models can be suitably modified to incorporate not only the age distribution but also their size. Applications of the modified capacitance model formulated here to calculate HTC show remarkable correspondence with experimentally obtained HTC values. The results address the shortcomings observed in HTC calculations by models that are based on a knowledge of fitted parameters and mathematically assumed age distributions. This suggests that the inferences about the flow structure patterns by EIM may be reliably used to quantitatively obtain intrinsic details about the hydrodynamics. Thus, it is shown here that for the CJR at the VL interface the age distribution is skewed and shifts toward the smaller eddies. Also, the age distributions can be compared to obtain the closest tank in series residence time distribution model (e.g., m ) 2 for VL interface and m ) 5 for SL interface). This again gives an estimate of the operating interfacial mechanisms in the CJR and JLR, and this information should help in reactor design and process optimization. An analogous formalism may be developed to study the mass transfer characteristics in chemical process equipment with interfacial gradients to complement the information about the transport pheonomena in these types of systems. Acknowledgment V.R.K. gratefully acknowledges the Department of Science and Technology, New Delhi, India, for the project SR/S3/CE/ 054/2003-SERC-Engg and the Center of Excellence in Scientific Computing (CoE-SC) at NCL for funding and computational facilities. The authors gratefully acknowledge the help rendered in coding the WTMM methodology for eddy identification by Neha Walani and Shalini Tripathi. Nomenclature a ) parameter in the temperature formulation for HFA Afilm ) area of film in the HFA probe, m2 b ) parameter in the temperature formulation for HFA c ) parameter in the temperature formulation for HFA Cp ) specific heat of fluid, J/(kg K) D ) tank diameter, m Ej ) jth eddy h ) heat transfer coefficient, W/(m2 K) hj ) average heat transfer coefficient predictions obtained based on theoretical models, W/(m2 K) hD ) heat transfer coefficient for Danckwerts model, W/(m2 K) hexp ) experimental heat transfer ccoefficient, W/(m2 K) hjexp ) average experimental heat transfer ccoefficient, W/(m2 K) hH ) heat transfer coefficient for Higbie model, W/(m2 K) HN ) nozzle clearance from the bottom in JLR, m I ) current, A

Ind. Eng. Chem. Res., Vol. 48, No. 21, 2009 k ) turbulent kinetic energy, m /s K ) thermal conductivity, W/(m K) kE,i ) kinetic energy of eddy for ith component of velocity, m2/s2 lE,i ) characteristic length scale of ith eddy, m jl ) length scale in single eddy model, m lI ) integral length scale, m m ) constant equivalent to number of tanks in Perlmutter model NE ) total number of eddies Nt ) total number of data points q ) heat flux at the interface, W/m2 qT ) total heat flux, W/m2 qw ) wire heat flux in HFA, W/m2 qj ) average heat flux, W/m2 R(τ) ) autocorrelation function Rfilm ) resistance in the probe, Ω Ret ) turbulent Reynolds number S ) surface renewal rate, 1/s t ) time, s tc ) mean eddy contact time, s tE,i ) characteristic age of ith eddy, s tI ) integral time scale, s t* ) autocorrelation time, s T ) temperature, K T0 ) initial temperature at t ) 0, K TB ) average bulk temperature, K Tfilm ) temperature of the film, K Tia,b ) CWT coefficient matrix TS ) surface temperature, K uE,i ) velocity of eddy for ith component, m/s uf ) fluid velocity, m/s ui ) instantaneous velocity in i direction, m/s ui′ ) fluctuating velocity in ith direction, m/s u2,rms ) velocity scale for large eddy model, m/s u2,τ ) friction velocity at the interface, u2,τ ) (τw/F)1/2, m/s ujE ) velocity scale in single eddy model, m/s uE,i ) characteristic eddy velocity for ith eddy, m/s xi ) coordinate direction, i ) 1, 2 radial/longitudinal direction and axial/transverse direction, respectively, m Greek Letters R ) thermal diffusivity, (k/FCP), m2/s ∆T ) temperature gradient, K ∆ti ) time gap between two successive crossings in EIM-ZC method, s ε ) turbulent energy dissipation rate, m2/s3 υ ) kinematic viscosity, m2/s F ) density of fluid, kg/m3 σ ) surface tension of fluid, N/m τ1, τ2 ) mean contact time for purlmutter model, s τw ) wall shear stress, N/m2 φ(t) ) age distribution function φ(t, AE) ) size (area) distribution function ψ(a,b) ) CWT basis function Subscripts and Superscripts j ) time averaged quantity exp ) experimental value E ) eddy i, j, k ) coordinates in generalized form with value 1, 2, and 3 corresponds to radial, axial, and tangential direction ′ ) fluctuating component AbbreVations CCA ) constant current anemometer CFD ) conputational fluid dynamics CJR ) condensation jet reactor CTA ) constant temperature anemometer 2

2

9439

CWT ) continuous wavelet transform EIM ) eddy identification method HFA ) hot film anemometer HTC ) heat transfer coefficient JLR ) jet loop reactor LDV ) laser Doppler velocimeter LL ) liquid-liquid MRA ) multiresolution analysis rms ) root-mean-square RTD ) residence time distribution SL ) solid-liquid VL ) vapor-liquid WT ) wavelet transform WTMM ) wavelet transform modulus maxima ZC ) zero crossing

Literature Cited (1) Dihn, T. N.; Bui, V. A.; Nourgaliev, R. R.; Green, J. A.; Sehgal, B. R. Experimental and analytical studies of melt jet-coolant interactions: a synthesis. Nucl. Eng. Des. 1999, 189, 299–327. (2) Jayanti, S. Hydrodynamics of jet mixing in vessel. Chem. Eng. Sci. 2001, 56, 193–210. (3) Patwardhan, A. W. CFD modeling of jet mixed tanks. Chem. Eng. Sci. 2002, 57, 1307–1318. (4) Kim, H. W.; Bae, Y. Y.; Song, C. H.; Park, J. K.; Choi, S. M. Experimental study on stable steam condensation in a quenching tank. Int. J. Energy Res. 2001, 25, 239–252. (5) Gulawani, S. S.; Deshpande, S. S.; Joshi, J. B.; Shah, M. S.; Prasad, C. S. R.; Shukla, D. S. Submerged gas jet into a liquid bath: A review. Ind. Eng. Chem. Res. 2007, 46, 3188–3218. (6) Koh, S. T.; Hiraoka, S.; Tada, Y.; Aragaki, T.; Yamada, I.; Takahashi, T.; Suzuki, K. Heat transfer in jet mixing vessel with rotating nozzle around the vessel axis. J. Chem. Eng. Jpn. 1990, 23, 627–632. (7) Stevens, J.; Webb, B. W. The effect of inclination on local heat transfer under an axisymmetric, free liquid jet. Int. J. Heat Mass Transfer 1991, 34, 1227–1236. (8) Daubner, M.; Batta, A.; Fellmoser, F.; Lefhalm, C. H.; Mack, K. J.; Stieglitz, R. Turbulent heat mixing of a heavy liquid metal flow within the MEGAPIE window geometry: The heated jet experiments. J. Nucl. Mater. 2004, 335, 286–292. (9) Simpson, M.; Chan, C. K. Hydrodynamics of a subsonic vapor jet in subcooled liquid. J. Heat Transfer 1982, 104, 271–278. (10) Jeje, A.; Asante, B.; Ross, B. Steam bubbling regimes and direct contact condensation heat transfer in highly subcooled water. Chem. Eng. Sci. 1990, 45, 639–650. (11) Aya, I.; Nariai, H. Evaluation of heat transfer coefficient at direct condensation of cold water and steam. Nucl. Eng. Des. 1991, 17, 131–146. (12) Liang, K. S.; Griffith, P. Experimental and analytical study of direct contact condensation of steam in water. Nucl. Eng. Des. 1994, 147, 131– 146. (13) Chun, H.; Kim, Y. K.; Park, J. W. An investigation of direct condensation of steam jet in subcooled water. Int. Commun. Heat Mass Transfer 1996, 23, 947–958. (14) Seong, H. J.; Hee, C. N.; Franz, M. Measurement of heat transfer coefficients for direct contact condensation in core makeup tanks using holographic interferometer. Nucl. Eng. Des. 2000, 199, 75–83. (15) Kim, Y. S.; Park, J. W.; Song, C. H. Investigation of the steamwater direct contact condensation heat transfer coefficient using interfacial transport models. Int. Commun. Heat Mass Transfer 2004, 31, 397–411. (16) Gulawani, S. S.; Joshi, J. B.; Shah, M. S.; Prasad, C. S. R.; Shukla, D. S. CFD analysis of flow pattern and heat transfer in direct contact steam condensation. Chem. Eng. Sci. 2006, 61, 5204–5220. (17) Wu, X. Z.; Yan, J. J.; Shao, S. F.; Cao, Y.; Liu, J. P. Experimental study on the condensation of supersonic steam jet submerged in quiescent subcooled water: steam plume shape and heat transfer. Int. J. Multiphase Flow 2007, 33, 1296–1307. (18) Banerjee, S. Turbulence structure and transport mechanisms at interface. Proc. 9th Int. Heat Transfer Conf. 1990, 5, 395–418. (19) Lewis, W. K.; Whitman, W. G. Principles of gas adsorption. Ind. Eng. Chem. 1924, 16, 1215–1220. (20) Higbie, R. The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. AIChE 1935, 31, 365–385. (21) Danckwerts, P. V. Significance of liquid film coefficient in gas. Ind. Eng. Chem. 1951, 43, 1460–1467.

9440


(22) Toor, H. L.; Marchello, J. M. Film penetration model for mass and heat transfer. AIChE J. 1958, 4, 97–99. (23) Harriott, P. A. Random eddy modification of penetration theory. Chem. Eng. Sci. 1962, 17, 149–165. (24) Fortuin, J. M. H.; Klijn, P. J. Drag reduction and surface renewal in turbulent pipe flow. Chem. Eng. Sci. 1982, 37, 611–623. (25) Fortuin, J. M. H.; Musschenga, E. E.; Hamersma, P. J. Transfer processes in turbulent pipe flow described by ERSR model. AIChE J. 1992, 38, 343–352. (26) Fortescue, G. E.; Pearson, J. R. A. On gas absorption into a turbulent liquid. Chem. Eng. Sci. 1967, 22, 1163–1176. (27) Banerjee, S.; Rhodes, E.; Scott, D. S. Mass transfer to falling wavy liquid films in turbulent flow. Ind. Eng. Chem. Fundam. 1968, 7, 22–27. (28) Lamont, J. C.; Scott, D. S. An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChE J. 1970, 16, 512–519. (29) Levich, W. G. Physicochemical hydrodynamics; Prentice Hall: Englewood Cliffs, NJ. (30) Blackwelder, R.; Kaplan, R. E. On the wall structure of the turbulent boundary layer. J. Fluid Mech. 1976, 76, 89–112. (31) Luk, S.; Lee, Y. H. Mass transfer in eddies close to air-water interface. AIChE J. 1986, 32, 1546–1555. (32) Theofaneous, T. G.; Houze, R. N.; Brumfield, L. K. Turbulent mass transfer at free gas-liquid interfaces with applications to open-channel, bubble and jet flows. Int. J. Heat Mass Transfer 1976, 19, 613–624. (33) Ghosh, A.; Badiger, M. V.; Tapadia, P. S.; Ravi Kumar, V.; Kulkarni, B. D. Characterization of chaotic dynamics-I: dynamical invariants of sheared polymer solutions. Chem. Eng. Sci. 2001, 56, 5615–5642. (34) Kulkarni, A. A.; Joshi, J. B.; Ravi Kumar, V.; Kulkarni, B. D. Identification of the principal time scales in bubble column by wavelet analysis. Chem. Eng. Sci. 2001, 56, 5739–5747. (35) Wang, D.; Ramagnoli, J. A. Robust multiscale pricinciple component analysis with application to process monitoring. J. Process Control 2005, 15, 869–882. (36) Roy, M.; Ravi Kumar, V.; Kulkarni, B. D.; Sanderson, J.; Rhodes, M.; Stappen, M. V. Simple denoising algorithm using wavelet transform. AIChE J. 1999, 45, 2461–2466. (37) Goring, D.; Nikora, V. I. Despiking acoustic Doppler velocimeter data. J. Hydrolic Eng. 2002, 128, 117–126. (38) Ganesam, R.; Das, T. K.; Venkatraman, V. Wavelet-based multiscale statistical process monitoring: A literature review. IIE Trans. 2004, 36, 787–806.

(39) Ravi Kumar, V.; Kulkarni, B. D.; Ghosh, A. Method and apparatus for online identification of safe operation and adVanced detection of unsafe operation of a process. US patent 6,826,513,2004. (40) Choi, S. W.; Morris, J.; Lee, I. Nonlinear multiscale modeling for fault detection and identification. Chem. Eng. Sci. 2008, 63, 2252–2266. (41) Meneveau, C.; Sreenivasan, K. Simple multifractal cascade model for fully developed turbulence. Phys. ReV. Lett. 1987, 59, 1424–1427. (42) Muzy, J.; Bacry, E.; Arneodo, A. Wavelets and multifractal formalism for singular signals: applications to turbulent data. Phys. ReV. Lett. 1991, 67, 3515–3518. (43) Arrault, J.; Arneodo, A.; Davis, A.; Marshak, A. Wavelet based multifractal analysis of rough surfaces: Application to cloud models and satellite data. Phys. ReV. Lett. 1997, 79, 75–78. (44) Camussi, R.; Guj, G. Orthonormal wavelet decomposition of turbulent flows: intermittency and coherent structures. J. Fluid Mech. 1997, 348, 177–199. (45) Kulkarni, A. A.; Joshi, J. B. Simultaneous measurement of flow pattern and mass transfer coefficient in bubble columns. Chem. Eng. Sci. 2004, 59, 271–281. (46) Deshpande, S. S.; Joshi, J. B.; Ravi Kumar, V.; Kulkarni, B. D. Identification and characterization of flow structures in chemical process equipment using multiresolution techniques. Chem. Eng. Sci. 2008. (47) Farge, M. Wavelet transforms and their applications to turbulence. Ann. ReV. Fluid Mech. 1992, 24, 395–457. (48) Bruun, H. H. Hot wire anemometry: principles and signal analysis; Oxford University Press: Oxford, 1996. (49) StreamLine/StreamWare: Installation and user’s manual; Dantec Dynamics A/S: Denmark, 2000. (50) Parcival, D. B.; Walden, A. T. WaVelet methods for time series analysis; Cambridge University Press: Cambridge, 2000. (51) Struzik, Z. R. Direct multifractal spectrum calculation from the wavelet transform. http://www.cwi.nl/ftp/CWIreports/INS/INS-R9914.ps.Z, 1999. (52) Perlmutter, D. D. Surface renewal models in mass transfer. Chem. Eng. Sci. 1961, 16, 287–296.

ReceiVed for reView January 13, 2009 ReVised manuscript receiVed April 26, 2009 Accepted April 29, 2009 IE900052S

Effect of Flow Structures on Heat Transfer in Single and Multiphase Jet

Recommend Documents