# Local-scale experimental investigation of a two-phase cross-flow in a tube bundle and flow-induced vibration: Intermittent/Churn flow

Giuseppe Spina, William Benguigui, G. Brillant, Daniele Vivaldi, Catherine Colin

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Giuseppe Spina, William Benguigui, G. Brillant, Daniele Vivaldi, Catherine Colin. Local-scale experimental investigation of a two-phase cross-flow in a tube bundle and flow-induced vibration: Intermittent/Churn flow. Journal of Fluids and Structures, 2025, 138, pp.104390. 10.1016/j.jfluidstructs.2025.104390. hal-05461904

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# Local-scale experimental investigation of a two-phase cross-flow in a tube bundle and flow-induced vibration: Intermittent/Churn flow

Giuseppe Spina<sup>a,d</sup>, William Benguigui<sup>b,c ID</sup>, Guillaume Brillant<sup>a ID</sup>, Daniele Vivaldi<sup>a</sup>, Catherine Colin<sup>d ID,*</sup>

## ARTICLE INFO

**Keywords:**

Two-phase flow

Flow induced vibration

CFD

Tube bundle

## ABSTRACT

Two-phase cross-flows in tube bundle can induce vibrations. This occurs in many industrial situations, such as nuclear power plant U-tube Steam Generator (SG). With the purpose of gathering high quality data for the validation of multiphase CFD simulation tools, a new experimental apparatus was designed and put in operation. The facility is instrumented for the two-phase air-water flow and tube vibration characterization. This article deals with experimental results in the churn/intermittent two-phase flow conditions. The experimental study was achieved by means of three measurement techniques: high-speed camera, optical dual-tip probe and wire mesh sensor. The behavior of the two-phase flow upstream of the tube bundle, characterized by the continuous generation of large gas structures, is detailed: high-speed camera and wire mesh sensor data reveal the prevalence of dispersed bubbles near the wall and large gas structures in the core region. The rising frequency of the large gas structures could be determined. Profiles of void fraction and gas velocity were measured within the tube bundle. The flow regime map of the experiment is proposed and is correlated with the study of flow-induced tube vibration. It highlights the role played by gas structure size distribution, thus flow pattern in the structural response in intermittent flow regimes with a local-scale characterization of the flow. Finally, the present work is a major contribution to improve and validate local-scale numerical simulation.

## 1. Introduction

For two-phase cross-flow in tube bundles, as void fraction increases the transition from bubbly flow to a so-called intermittent flow was identified by several authors. Nakamura et al. (1995b,a) examined the impact of intermittent two-phase flow: his experiments demonstrate an increase in excitation force magnitude in the intermittent slug flow regime. The intermittent nature of these forces complicates the analytical determination of the fluid-elastic instability (FEI) threshold. Pettigrew et al. (1989a,b) experimental results in different array geometries reveal differences in the instability behavior for various flow regimes. In subsequent studies, Pettigrew et al. (1995, 2002) used a tube bundle with a pitch ratio (P/D with P the distance between two cylinder center and D their diameter) of 1.5 under Freon two-phase flow. They observed a decrease in the mass flux required for

<footnote><sup>a</sup> Autorité de Sureté nucléaire et de radioprotection (ASNR), Cadarache, St Paul-lez-Durance, BP3, 13115, France</footnote>

<footnote><sup>b</sup> Électricité de France (EDF), 6 Quai Watier 78401 Chatou Cedex, France</footnote>

<footnote><sup>c</sup> IMSIA, UMR EDF-ENSTA-CNRS 9219, Paris-Saclay university, 91762, Palaiseau, France</footnote>

<footnote><sup>d</sup> Institut de Mécanique des Fluides de Toulouse, Université de Toulouse, CNRS, INPT, UPS, Allée du Prof. Camille Soula, 31400 Toulouse, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: catherine.colin@toulouse-inp.fr (C. Colin).</footnote>
instability as void fraction exceeds approximately 60%, suggesting that the specific flow regime influences the stability threshold. Pettigrew et al. (1989a) found that hydrodynamic mass in air-water two-phase flow aligns with theoretical expectations when void fractions are below approximately 80%; however, a deviation occurs when void fraction exceeds 80%, attributed to intermittent flow. Feenstra et al. (1995, 2002) found the void fraction to be an important parameter for the stability criteria, and developed a new correlation to estimate the void fraction inside a tube bundle. They then applied their model to calculate parameters for Connors' formula (Connors, 1970), comparing them with the Homogeneous Equilibrium Model (HEM): their model eliminates the previously noted discontinuity in the *K* factor as the flow transitions from bubbly to intermittent. In contrast to the application of the HEM model, when applying their void fraction model, the authors also showed that the relationship between the mass-damping parameter and the reduced velocity parameter remains linear entering the intermittent flow regime. Hirota et al. (2002) found well-defined FEI in bubbly two-phase flow but not in intermittent flow, highlighting the emergence of intermittent instability. Ricciardi et al. (2011) conducted an experimental study to explore the distinction between instability in the lift and drag directions; they emphasized the importance of investigating the flow regime to gain insights into FEI in two-phase flow. Zhang (2007) measured the forces acting on tubes in air-water cross-flow, and quasi-periodic forces in both drag and lift directions, with larger forces observed along the drag direction. The observed forces corresponded to periodic flow patterns such as slug and intermittent flow.

These experimental studies reveal that understanding all factors contributing to FEI in two-phase flow remains a challenge. The complexity of two-phase flows, especially actual flow patterns and regime transitions, significantly influences the instability as shown in a recent review of literature from Benguigui et al. (2024). Adapting semi-empirical formulas designed for single-phase flow FEI onset to two-phase cross-flow proves to be complicated. Critical parameters like hydrodynamic mass and two-phase damping require empirical formulas, necessitating experimental validation. For this reason, some authors realized experimental campaigns dedicated to explore the two-phase flow behavior within tube bundle cross-flow configurations. Grant and Chisholm (1979) employed a facility containing a normal triangular tube bundle 4 × 10 with $P/D = 1.25$ and $D = 19$ mm, establishing the different flow regimes by visual observations. Ulbrich and Mewes (1994) used a square pitch bundle of 5 × 10 tubes with $P/D = 1.5$ and $D = 20$ mm. They employed measurements of two-phase mixture pressure drop to assess fluctuations in the void fraction over time. The variation of pressure drop over time exhibits differences for the different flow patterns. By comparing pressure drop measurements with visual observations using photographic techniques and video cameras, the researchers were able to construct a flow regime map, providing a detailed description of the different flow patterns and their transitional regimes. The research conducted by Xu et al. (1998) focused on a 3 × 20 tube bundle with $P/D = 1.28$ and $D = 9.79$ mm. Pressure drop measurements were utilized to determine the average void fraction, while visual observations were used to construct the flow regime map. Noghrehkar et al. (1999) conducted experiments to characterize the two-phase flow inside both in-line and staggered 5 × 24 tube bundles with $P/D = 1.47$ and $D = 12.7$ mm. They utilized local void fraction measurements and the probability density function (PDF) method to identify the two-phase flow regimes. The results obtained for the in-line tube bundle were compared to those reported in the open literature, particularly the findings of Ulbrich and Mewes (1994): discrepancies were observed due to different measurement techniques and bundle geometries. Murakawa et al. (2016) performed experiments in both in-line and staggered 4 × 8 tube bundles with $P/D = 1.5$ and $D = 15$ mm. They utilized X-ray radiography and visual observations to obtain two-dimensional void fraction distribution and constructed flow regime maps in a tube bundle. The flow regime maps were found to be in good agreement with the existing literature. The experimental results were compared with the correlation proposed by Feenstra et al. (2000) for predicting the void fraction in a tube bundle. The correlation was found to be in agreement with the experimental data. The test section used by Kanizawa et al. (2016) was a normal triangular 4 × 20 tube bundle with $P/D = 1.26$ and $D = 19$ mm. Kanizawa et al. (2016) subjectively identified flow patterns through visual observation and objectively using the k-means clustering method based on signals from a differential pressure transducer and a capacitive sensor. They demonstrated that utilizing different identification methods for determining the flow regime results in different flow regime maps. They also proposed a new method for predicting flow patterns, based on balancing the dominant forces of the two-phase flow. The method was compared with experimental results and findings from the literature, showing satisfactory agreement. Aprin et al. (2011) investigated two-phase flow patterns in a staggered 5 × 9 tube bundle with $P/D = 1.33$ and $D = 19.05$ mm, for three hydrocarbons at boiling conditions. The authors measured local void fraction through an optical probe. A quantitative method, based on PDF of void fraction, for analyzing flow structures was proposed. Statistical analysis identified bubbly and annular-dispersed flow regimes, with transitions at specific void fraction thresholds. A flow map based on vapor and liquid velocities was presented. The same methodology and instrumentation was used by Piteau et al. (2022) to identify flow regime in a square tube bundle subjected to water-air two phase flow. The test section contained 5 × 3 tubes with $P/D = 1.5$ and $D = 30$ mm. All these experimental campaigns allowed to identify at least three different two-phase flow regimes: bubbly, intermittent and annular flows.

Despite two-phase flow regime identification realized by these authors, local experimental measurements of two-phase parameters such as void fraction and velocities have not been reported in the literature. This kind of measurements are necessary to understand void fraction space and time distribution and phase-velocities in different two-phase flow regimes. These features represent the underlying mechanisms of the fluid-induced forces. Moreover, these details are necessary to assess the consistency of two-phase CFD results, that have recently been applied to cross-flow in tube bundles (Benguigui et al., 2017; Sadek et al., 2018; De Santis et al., 2021). CFD simulations can represent a powerful tool to study the impact of tube bundle geometrical configuration (pitch configuration, pitch-over-diameter ratio, etc.) and thermodynamic conditions (air-water versus prototypical steam-water mixture), hardly accessible experimentally due to cost and technical feasibility. However, CFD requires dedicated CFD-grade experimental results for a preliminary validation. The TREFLE (Two-phase flow REgimes and FLuid-structure interaction Experimental) facility was recently built (Spina et al., 2025) with the goal of generating this type of experimental results. TREFLE contains a 5 × 5, square-pitch, horizontal straight tube bundle test section, subjected to a vertical air-water flow. Similarly to many
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Layout of the TREFLE facility with details of instrumentation (Fig. 1(a)). Details of the test section (Fig. 1(b)). In red the central tube to be substituted with the vibrating tube. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

authors, the choice to use air/water was retained, allowing to work at atmospheric conditions, which helps in terms of mechanical design and in terms of visual (possibility of using transparent windows) and intrusive (less challenging conditions for employing flow measuring devices) study of the flow. Results in bubbly flow were previously published by Spina et al. (2025), who measured profiles of void fraction and gas velocity in different positions inside the tube bundle, and vibrations of one tube. As a following step, an experimental campaign in churn/intermittent two-phase flow (higher gas velocities than in bubbly flow) was realized: the present paper presents the results obtained. We first focused on the determination of two-phase features, such as intermittent slug frequency, void fraction and gas velocities between the tubes. Then, the flow-induced vibrations were measured for a configuration with one flexible tube surrounded by fixed tubes. We attempted to find the vibration response characteristics as a function of the two-phase flow regime.

## 2. Experimental set-up

In Fig. 1, the experimental facility TREFLE is shown, where water is provided through a divergent section. To achieve a uniform water velocity profile at the facility inlet, a honeycomb and several plates are inserted within the divergent section. Air is introduced into the facility through a gas injector. Details of the facility design can be found in Spina et al. (2025).

The test section contains an in-line square pitch 5 × 5 tube bundle with P/D = 1.44, consisting of non-vibrating tubes. The tube length (L) is 10 times the tube diameter, which is 30 mm. The central tube is designed to be replaced with a vibrating one (Spina et al., 2025). The facility features large transparent windows for flow visualization. The air injection includes a control valve to regulate the air flow rate, and the uncertainty associated with the control valve varies depending on the specific flow rate, as specified in Table 1. The gas injector used in this study contains seven pierced tubes with an outer diameter (O.D.) of 25 mm. Each pipe has 60 holes on the top with a diameter of 5 mm. The studied flow rates and test matrix are detailed in Table 1. Tests T1 to T4 lie in the bubbly flow regime region were previously presented by Spina et al. (2025). The experiments are conducted with water flow rates of $\dot{m}_w = 2500 \text{ g s}^{-1}$ and air flow rates ranging from $10 < \dot{m}_a < 29 \text{ g s}^{-1}$. This corresponds to a water gap superficial velocity of $J_l = 0.126 \text{ m s}^{-1}$ and an air gap superficial velocity in the range of $0.42 < J_g < 1.22 \text{ m s}^{-1}$. The generic superficial gap velocity is computed with $J = \frac{m}{\rho S}$ where S is the minimum flow area between the tubes, ρ is the phase density, and $\dot{m}$ is the generic mass flow rate. Considering b and c the width and depth of the free duct, respectively, the generic free duct superficial velocity ($U_s$) is calculated as $U_s = \frac{m}{\rho b c}$.

A fiber bi-optical probe (developed by RBI Instrumentation) was used (pictures of its geometric parameters and positioning inside the tube bundle are given in Fig. 25). The measurement points presented in Fig. 1(a) enable the construction of vertical profiles of
<table><caption>**Table 1**
Experimental test conditions.</caption><thead><tr><th>Test no.</th><th>Air flow rate<br>g s<sup>-1</sup></th><th>Water flow rate<br>g s<sup>-1</sup></th><th>J<sub>l</sub><br>m s<sup>-1</sup></th><th>J<sub>g</sub><br>m s<sup>-1</sup></th><th>U<sub>sl</sub><br>m s<sup>-1</sup></th><th>U<sub>sg</sub><br>m s<sup>-1</sup></th></tr></thead><tbody><tr><td>T1</td><td>0.5 ± 0.0025</td><td>2500 ± 10</td><td>0.126</td><td>0.021</td><td>0.039</td><td>0.007</td></tr><tr><td>T2</td><td>1.0 ± 0.005</td><td>2500 ± 10</td><td>0.126</td><td>0.042</td><td>0.039</td><td>0.013</td></tr><tr><td>T3</td><td>2.0 ± 0.01</td><td>2500 ± 10</td><td>0.126</td><td>0.084</td><td>0.039</td><td>0.026</td></tr><tr><td>T4</td><td>4.0 ± 0.02</td><td>2500 ± 10</td><td>0.126</td><td>0.168</td><td>0.039</td><td>0.051</td></tr><tr><td>T5</td><td>10 ± 0.35</td><td>2500 ± 10</td><td>0.126</td><td>0.420</td><td>0.039</td><td>0.135</td></tr><tr><td>T6</td><td>16 ± 0.85</td><td>2500 ± 10</td><td>0.126</td><td>0.673</td><td>0.039</td><td>0.212</td></tr><tr><td>T7</td><td>29 ± 0.65</td><td>2500 ± 10</td><td>0.126</td><td>1.220</td><td>0.039</td><td>0.373</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Wire Mesh Sensor installed on TREFLE facility (geometric parameters are in Appendix in Fig. 26).</figcaption></figure>

void fraction, air velocity and bubble mean Sauter diameter. The void fraction is calculated as $α = T_g/(T_l + T_g)$, where $T_g$ and $T_l$ represent the total gas and liquid time recorded from one tip of the probe, respectively. The Sauter mean diameter ($d_{sm}$) is calculated as $d_{sm} = 6α/A_l$, where $A_l$ corresponds to the interfacial area value calculated according to Kataoka et al. (1986). The average bubble velocity ($v_b$) is determined as $v_b = d/T_{flight}$, taking into account the distance between the primary and secondary tips ($d$) and the average transit time required for bubbles to travel from the reference sensor to the secondary sensor ($T_{flight}$). The average transit time is obtained by cross-correlating the signals from the two tips. Further details regarding the measured quantities via the optical probe can be found in Garnier (1997). Signal acquisition yields the “phase-time histogram”, which represents the distribution of recorded gas residence time and liquid residence time on the probe tip. Multiplying each gas-time by the velocity results in the histogram of intercepted chord lengths. By employing a mathematical model that considers the non-spherical nature of bubbles (as described by Garnier (1997)), the “bubble size distribution” can be obtained.

A wire mesh sensor (WMS) was used and presented in Fig. 2. The WMS contains 78 × 56 wires with a spatial resolution of 3.95 × 4.00 mm. The working principle of the WMS is based on the measurement of the local instantaneous conductivity of the two-phase mixture (Prasser et al., 1998).

### 3. Two-phase flow characterization: tube bundle inlet

To explore the two-phase flow upstream of the tube bundle, videos were recorded using a high-speed camera. Despite the highly chaotic two-phase flow, it is possible to perform a qualitative analysis of the flow.

Fig. 3 displays snapshots captured upstream of the tube bundles (window W1 in Fig. 1(a)). These images predominantly reveal dispersed bubbles near the wall, occasionally interspersed with larger gas structures. Based on video analysis, it appears that the
<figure><img src="image_7.png" /><figcaption>Fig. 3. Photos upstream the tube bundle, form visualization windows W2 in Fig. 1.</figcaption></figure>

presence of large gas structures is concentrated in the bulk region (central region of the test section). An intriguing observation emerged during the analysis of the videos recorded by the high-speed camera: the downward motion of bubbles close to the wall.

Given the substantial dimensions of the section (300 × 216 mm), relying solely on the analysis of external images to investigate this type of regime in two-phase flow is not enough. A more comprehensive examination can be achieved by analyzing data collected from the WMS. The WMS was strategically positioned approximately 260 mm below the tube bundle to minimize any interference from its presence. To determine the appropriate acquisition frequency and time, several tests were conducted. Utilizing the results from the optic probe placed upstream of the tube bundle, the average gas transition time ($g_t$) can be evaluated by dividing the Sauter mean diameter ($d_{sm}$) by the average gas velocity ($v_g$), as expressed in Eq. (1).

$$g_t = \frac{d_{sm}}{v_g} \qquad (1)$$

By multiplying the gas transition time by the acquisition frequency ($f_a$), we can estimate how many times one gas structure (of average size) is recorded by the WMS along its path (Eq. (2)).

$$n_B = g_t \cdot f_a \qquad (2)$$

For test T7, with a frequency of 1000 Hz, a general gas structure is recorded 10 times on average in one second of acquisition. This frequency was determined to be a suitable compromise between result accuracy and storage memory usage. The time duration of acquisition was set to be in the same order of magnitude as the optical probe acquisitions, specifically 800 s.

Analyzing the instantaneous two-dimensional (2D) void fraction distribution provides valuable insights into the flow structure. To understand how the flow structure evolves during the experiments, virtual cross-sectional side-views can be generated. These side-views are obtained by extracting the void fraction distribution across the cross-section of the duct from the 2D distribution. Subsequently, time series of these distributions are arranged as lines in a vertical sequence, where the z-axis indicates the time scale. However, the time axis can be transformed into a virtual z*-axis by scaling it with the average velocity of the gas phase, derived from the space- and time-averaged void fraction ($\bar{a}$), as expressed in Eq. (3).

$$z^* = \frac{t \cdot U_{sg}}{\bar{a}} \qquad (3)$$

Figs. 4 and 5 display snapshots of the 2D void fraction distribution obtained from the WMS, along with their corresponding side-views. For tests T5, T6, and T7, a uniform time scale of 1 s (equivalent to 1000 frames) was employed. The z*-axis varies among the different tests due to the dependence of Eq. (3) on $U_{sg}$ and $\bar{a}$, which vary for each specific test.

From Figs. 4 and 5, the two-phase flow morphology is of churn flow type with large gas structures. The flow exhibits a chaotic, churning behavior, and the large gas structures appear irregularly distributed. From the image analysis, it is clear that large gas structures mostly arise in the central region of the flow.

A more quantitative analysis can confirm these results. Fig. 6 presents the 2D distributions of the time-averaged void fraction ($\bar{a}(x, y)$) from WMS measurements for the different tests T5, T6, and T7.
<figure><img src="image_8.png" /><figcaption>Fig. 4. Void fraction distribution upstream the tube bundle, cross-sectional distribution of the void fraction.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 5. Void fraction distribution upstream the tube bundle, y-side view of the void fraction evolution, x = 0.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6. Time average of void fraction 2D distribution $\bar{a}(x, y)$ from WMS (x and y represent here the number of WMS wire in the two directions).</figcaption></figure>

The void fraction at every point (x, y) within the WMS grid is averaged over an 800-s duration. As observed in the tests, the substantial presence of large gas structures in the central region of the flow notably influences the void fraction distribution. This influence manifests as a distinct peak in the central region and a reduction in the near-wall region. This behavior is also clear in the time-averaged radial distribution of void fraction, denoted as $\bar{a}(r)$, as illustrated in Fig. 7.

Analyzing the space-averaged void fraction provides valuable insights into the characteristics of two-phase flow ($\bar{a}(t)$ from WMS measurements). Fig. 8 presents the evolution of the void fraction over time, only part of the signal is displayed for a more comprehensive understanding.

Fig. 8(a) shows a comparison between the different tests, illustrating a signal that exhibits an average increase with higher air flow rates. The signal displays peaks and depressions, as highlighted in Fig. 8(b). The peaks correspond to the passage of large gas structures, while the depressions correspond to the dispersed phase. Employing this approach, the two-phase flow can be investigated
<figure><img src="image_11.png" /><figcaption>Fig. 7. Time-average of the radial distribution of the void fraction $\bar{a}(r)$ from WMS.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(a) Comparison between the tests during 5 seconds.</figcaption></figure>

<caption>(b) 1-second zoom for test T6.</caption>

<figure><img src="image_13.png" /><figcaption>Fig. 9. Power spectral density (PSD) of $\bar{a}(t)$ for tests T5, T6, T7 from WMS measurements.</figcaption></figure>

by the power spectral density (PSD) of the signal representing the evolution of the space-averaged void fraction, denoted as $\bar{a}(t)$. The PSD results are presented in Fig. 9.

The PSD reveals a pronounced peak around 3 Hz for all tests: 3.4 Hz for test T5, 3.5 Hz for test T6, and 3.2 Hz for test T7. This frequency is indicative of the characteristic frequency associated with the passage of large gas structures within the flow. The PSD was derived by optimizing Hann windows, yet, due to the smoothness of the peak, determining whether the identified frequency precisely represents the value or if the mentioned values are within an order of magnitude is challenging. In fact, a fast Fourier
<figure><img src="image_14.png" /><figcaption>Fig. 10. PSD of $\alpha(t)$ obtained with the optical probe for $\Delta t = 0.001$ s over 1000 s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

transform reveals that the peak in the PSD encompasses a set of peaks ranging from 3 Hz to 4 Hz. An intriguing observation is the presence of periodicity in the large gas structure, that appears relatively independent of the air flow rate.

The optical probe could be placed upstream of the tube bundle, approximately 110 mm below the last row of tubes, to investigate the inlet conditions. To obtain a time-varying evolution of the void fraction $\alpha(t)$ and enable similar analysis as the space-averaged void fraction evolution $\bar{a}(t)$ obtained from the WMS, the probe signal, acquired at a frequency of 20 kHz, was integrated over a time window $\Delta t$. The void fraction time-evolution ($\alpha(t)$) was calculated using the gas time over a small time window ($T_g(\Delta t)$), hence $\alpha(t) = T_g(\Delta t)/\Delta t$. This integration allows for the calculation of the void fraction evolution with time. To facilitate the comparison, the integration time window was set to $\Delta t = 0.001$, ensuring that it matches the acquisition frequency of the WMS (1000 Hz). Fig. 10 presents the PSD of the void fraction time-evolution for tests T5, T6 and T7, with a sample of the time-evolution of the void fraction highlighting the presence of large gas structures.

The optical probe provides a localized measurement of the void fraction in the core of the flow, while the WMS yields a surface-averaged distribution. However, when assessing the two measurement systems in terms of recording the frequency of large gas structures, it proves to be a reliable approach. Indeed, a closer examination of the post-processed probe signal in Fig. 10(b) reveals (indicated by red rectangles) the large structures recorded through this specific post-processing method. The PSD derived from the probe in Fig. 10(a) shows similar results as the ones obtained with the WMS (Fig. 9). Notably, the PSD exhibits a frequency peak around 3 Hz, indicating that the frequency of passage of large structures is confirmed by the optical probe measurements in the center of the channel.

Both the WMS and optical probe offer insights into the size of bubbles/large gas structures. Fig. 11 illustrates the Probability Density Function (PDF) of the bubble size distribution obtained through both the WMS and optical probe. Analyzing a PDF of bubble sizes can yield valuable information about the characteristics and distribution of the bubble population. It is important to acknowledge that the two measurement systems employ different methods for calculating bubble sizes, and they differ not only in their approach (a local measurement through the optical probe and a two-dimensional measurement through the WMS) but also in their limitations. Notably, differences may arise, such as the minimum diameter detected, limited by the mesh for the WMS and by the distance between the tips for the probe.

In Fig. 11, both measurement systems identify bubble sizes characterized by a PDF peak composed of small dispersed bubbles in the order of a few millimeters. This is accompanied by a tail representing the contribution of large gas structures in all the tests. The lengths of both the tails and peaks progressively increase from test T5 to test T7 for both the optical probe and WMS results. Nevertheless, the peaks corresponding to dispersed bubbles consistently remain around the same values. Specifically, several peaks between 3 mm and 5 mm are detected for the WMS results, while the optical probe results show a peak around 1.5 mm. This behavior suggests an augmentation in the number of dispersed bubbles of the same size and an enlargement of the large gas structures. The constant sizes of dispersed bubbles across all tests may be attributed to reaching the critical Weber number, limiting further growth.

The primary difference between the optical probe and WMS results lies in the dispersed bubble peak, which appears shifted towards smaller values in the optical probe results. However, as noted by Kiambi et al. (2003), measurements of bubble size by the optical probe during chaotic two-phase flows may not be entirely reliable. The recirculations upstream of the bundle can affect measurements, potentially causing the flow not to align precisely with the probe tips. Additionally, in the case of the optical probe, bubble size is not directly detected, it is post-processed using the distribution of recorded gas residence time and gas velocity to derive the bubble size distribution. Consequently, while the qualitative shape of the PDF remains similar between the two measurement systems, the average diameter differs.

To gain further insights into the characteristics and contribution of large gas structures, the WMS measurements allow the extraction of the bubble size contribution to the void fraction, represented as $\Delta\alpha_i/\Delta d_{Bi}$ (void fraction of the bubbles of this class referring to bubble class). The bubble diameters were discretized considering a $\Delta d_B = 0.25$ mm, hence, the number of class of void
<figure><img src="image_15.png" /><figcaption>**Fig. 11.** Comparison of PDF of bubble size distribution obtained with optical probe (OP) and WMS. The average diameter $\bar{d}_B$ is obtained according to: $\bar{d}_B = \sum d_B \cdot P(d_B)/ \sum P(d_B)$.</figcaption></figure>

<caption>**Table 2**</caption>

Summary of average data obtained from WMS and optical probe. $\bar{a}$ is the average void fraction. $\bar{a}_c$ indicates the void fraction detected in the center of the flow by the WMS (Fig. 6). $\bar{d}_B$ is the average diameter, $d_{sm}$ is the sauter mean diameter and $v_B$ is the gas phase velocity.

<table><thead><tr><th rowspan="2">Test no.</th><th>WMS</th><th>WMS center</th><th>Probe</th><th>WMS</th><th>Probe</th><th>Probe</th></tr><tr><th>ā<br/>[-]</th><th>āc<br/>[-]</th><th>ā<br/>[-]</th><th>d&#773;<sub>B</sub><br/>[mm]</th><th>d&#773;<sub>sm</sub><br/>[mm]</th><th>v<sub>B</sub><br/>[m s<sup>-1</sup>]</th></tr></thead><tbody><tr><td>T5</td><td>0.20</td><td>0.30</td><td>0.28</td><td>5.4</td><td>9.0</td><td>1.17</td></tr><tr><td>T6</td><td>0.24</td><td>0.38</td><td>0.35</td><td>5.8</td><td>9.5</td><td>1.31</td></tr><tr><td>T7</td><td>0.33</td><td>0.52</td><td>0.51</td><td>6.3</td><td>10.4</td><td>1.51</td></tr></tbody></table>

fraction was adapted at the number of class of diameters. The corresponding results are presented in Fig. 12. Bubble size distributions are constructed by summarizing the contributions of bubbles within specific diameter ranges to the integral void fraction. These partial void fractions, denoted as $\Delta\alpha_i/\Delta d_{Bi}$, are plotted against the equivalent bubble diameter, $\Delta d_{Bi}$. Integrating over this type of bubble size distribution yields the average void fraction ($\bar{a} = \sum \Delta\alpha_i$). Often, the resulting curves exhibit unevenness at larger diameters due to the presence of only a few large bubbles, which account for most of the void fraction.

From this type of bubble size presentation, four distinct peaks can be observed in all tests. The peaks are highlighted through an envelope of the histograms. The first peak (P1) corresponds to dispersed bubbles around 4 mm. The second peak (P2) increases its prominence as the air flow rate increases from the T5 to T7 tests, reaching sizes on the order of 20 mm. The third peak (P3) shows a progressive increase in size and power from the T5 to T7 tests, ranging between 40 mm and 50 mm. Finally, the fourth peak becomes more pronounced as the air flow rate increases from test T5 to T7, indicating sizes greater than 60 mm. The last three peaks shift towards larger values as the tests progress from T5 to T7, suggesting the presence of three distinct types of large gas structures. The data collected with WMS and optical probe can be summarized in Table 2.

The comparison reveals clear discrepancies between the optical probe and WMS results, attributed to differences in measured quantities. These disparities can in fact be attributed to the placement of the optical probe in the center of the two-phase flow, enabling local measurements, while the WMS provides 2D averaged quantities. Under these conditions, where the two-phase flow is not spatially homogeneous, substantial differences in the results arise. Specifically, the large gas structures tend to flow in the center of the flow, while the dispersed bubbles are distributed around them. As a result, the probe detects significantly larger diameters
<figure><img src="image_16.png" /><figcaption>Fig. 12. Plot of the contribution of bubble size to the void fraction, $\Delta a_i/\Delta d_{Bi}$, as a function of bubble size.</figcaption></figure>

and void fractions compared to the measurements obtained by the WMS in the entire section ($\bar{a}$). In fact, the void fraction measured by the probe closely aligns with the void fraction detected in the center of the flow by the WMS $\bar{\alpha}_c$ (Fig. 6). Additionally, it should be noted that measurements of bubble size by the optical probe during chaotic two-phase flows are not entirely reliable, while gas velocity measurements are more accurate but have large uncertainties. Moreover, an oscillating phenomenon is observed in the ascending gas structures, in which large gas structures move back and forth horizontally. Consequently, the probe, with its fixed measurement point, may also overlook some of these substantial structures.

Based on the findings in this section, we classify the flow regime in the free duct for test T5, T6, and T7 as churn flow. Churn flow, according to Taitel et al. (1980) definition, is characterized as chaotic, frothy, and disordered. In this flow regime, the large gas structures become distorted, and the continuity of the liquid between successive large gas structures is frequently disrupted due to high local gas concentrations. This disruption causes liquid slugs to fall, accumulate, form bridges, and then be lifted by the gas. A distinctive feature of churn flow is the oscillatory or alternating direction of liquid motion. Some observers describe this regime as resembling a froth flow pattern with finer dispersion.

The investigation of the inlet conditions to the tube bundle involved studying the two-phase flow in the free duct. This analysis may contribute to a better understanding of the two-phase flow within the tube bundle. The subsequent section presents the detailed analysis of the two-phase flow within the tube bundle.

## 4. Two-phase flow characterization within the tube bundle

After characterizing the two-phase flow upstream of the tube bundle, the analysis shifts towards examining the behavior of the two-phase flow within the tube bundle. Understanding the two-phase flow dynamics upstream of the tube bundle provides valuable insights into how the flow conditions in the free section influence the behavior inside the tube bundle. The objective in this phase is to utilize the optical probe and fast camera to experimentally investigate the behavior of the two-phase flow within the tube bundle. Visual observations of the intermittent flow regime within the tube bundle during tests T5, T6, and T7 are depicted in Fig. 13 (windows W2 in Fig. 1(a)).

The images reveal an intriguing distribution pattern within the two-phase flow. The majority of small dispersed bubbles exhibit a tendency to accumulate near the wall, while larger gas structures are observable behind them. This distribution pattern is a direct outcome of the inlet condition. The churn-like flow observed upstream of the tube bundle, characterized by prominent gas structures in the core of the flow, persists within the bundle. However, upon encountering the obstacle posed by the tube bundle, the large
<figure><img src="image_17.png" /><figcaption>Fig. 13. Images within the tube bundle, form visualization windows W2 in Fig. 1(a).</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 14. Images within the tube bundle, form visualization windows W3 in Fig. 1(a).</figcaption></figure>

gas structures undergo disruption, as evident in the lateral views of the tube bundle presented in Fig. 14, in comparison with the images obtained using the WMS (Fig. 4).

The images show large gas structures that undergo shape distortion upon entering the tube bundle (refer to Figs. 4 and 5, for images upstream of the tube bundle). Various definitions of this flow regime exist within flow regime maps. Some authors, such as Piteau et al. (2022), Kanizawa et al. (2016), Mao and Hibiki (2017), and Chu et al. (2011), define a transition between the bubbly and churn/slug flow regimes. In contrast, Grant and Chisholm (1979), Ulbrich and Mewes (1994), Noghrehkar et al. (1999), and Murakawa et al. (2016) establish a transition between the bubbly and intermittent flow regimes.

In the current study, the flow regime, as determined through qualitative analysis using the fast camera, can be characterized as a churn-like flow regime. This is characterized by the simultaneous presence of both large gas structures and dispersed bubbles within a continuous liquid phase. However, due to the observed periodic intermittence during the passage of large gas structures upstream of the tube bundle, the video footage also reveals intermittent-like behavior in the flow. This involves distinct large gas structures alternating with the liquid phase, even within the bundle itself.

To further investigate this behavior, the application of optical probes for void fraction measurements becomes significant. As discussed in Section 3, the signal obtained from the optical probe can be discretized over a time interval $\Delta t$ (set to 0.001 s in this case). In this specific instance, we focus on measurement point 2 (Fig. 1(a)), situated within the tube bundle, specifically in the gap between the central tube and its adjacent counterpart. The Power Spectral Density (PSD) of the void fraction fluctuation is presented in Fig. 15.

The PSD analysis, for tests T5, T6 and T7, reveals prominent peaks occurring at frequencies approximately around 3 Hz. These frequencies can be attributed to the passage frequency of the large gas structures within the tube bundle. A comparison of this PSD analysis with the PSD obtained upstream of the tube bundle (Figs. 9 and 10) demonstrates that the signal obtained is similar in terms of the frequency of void fraction oscillations. This signal reflects the bundle inlet conditions, as the frequency of large gas structures remains similar inside the tube bundle. This behavior leads to an intermittent nature of the flow.

From this analysis, a significant conclusion can be drawn: the interaction between the gas and liquid phases, the influence of inlet conditions, and the obstructive nature of the tube bundle all contribute to the potential overlap of churn flow and intermittent flow regimes. The presence of obstacles created by the tube bundle disrupts the flow dynamics and can result in the breakup of large gas structures characteristic of churn flow. This disruption leads to the formation of intermittent flow patterns within the tube bundle, where distinct slugs or bubbles of gas and liquid coexist.

Vertical profiles of void fraction, gas velocity and sauter mean diameter can be obtained from the probe measurement points 1, 8, 2, 3, 4, 5 in Fig. 1.
<figure><img src="image_19.png" /><figcaption>Fig. 15. PSD of void fraction evolution within the tube bundle obtained by the OP signal.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 16. Vertical profiles of void fraction and gas velocity obtained with optical probe within the tube bundle.</figcaption></figure>

In Fig. 16, in the vertical profile, it is evident that the void fraction increases when transitioning from upstream of the tube bundle to within the bundle. The larger void fraction within the tube bundle is coherent with the decrease of the cross-section and the measurement of a smaller gas velocity, compared to the measurements upstream. However, the void fraction inside the tube bundle is only significantly affected by the bundle geometry in test T5, where it increases as the flow area decreases and vice versa. On the other hand, for tests T6 and T7, the void fraction is less influenced by the bundle geometry and tends to remain constant.

The evolution of gas velocity within the bundle, as depicted in Fig. 16(b), supports the notion that a smaller flow area leads to a larger flow velocity. However, upstream of the tube bundle, the gas velocity is larger than within the bundle. This behavior is attributed to the presence of large gas structures in this regime. Due to the substantial size of these gas structures and the relatively low liquid velocity, the two-phase flow upstream is primarily buoyancy-driven. As the gas structures move into the tube bundle, they undergo fragmentation or breakup. The smaller size of gas bubbles inside the bundle reduces their buoyancy effect. Smaller bubbles have less buoyancy force acting on them compared to larger ones. Consequently, within the tube bundle, the buoyancy-driven component of the flow becomes weaker and the gas velocity decreases.

The experimental campaign conducted to explore the intermittent flow regime has revealed intriguing findings, particularly in relation to the void fraction parameter. While many experiments documented in the literature have focused on studying tube vibration response and Fluid-Elastic Instability, these studies often rely on two-phase flow information using the Homogeneous Equilibrium model (HEM) (Pettigrew et al., 1989a,b; Axisa et al., 1990, 1985; Delaune et al., 2018). However, this model, which assumes equal gas and liquid velocities, proves inadequate as the phase slip intensifies. In the context of water-air two-phase flow under ambient temperature and pressure conditions, such as in our present experimental campaign, the HEM model cannot accurately estimate the void fraction as reported in Fig. 17. The plot reports experimental data presented in this work and bubbly
<figure><img src="image_21.png" /><figcaption>Fig. 17. Void fraction comparison among the model from Feenstra et al. (2000), the HEM model and experimental results obtained by optical probe at point 2 for a liquid superficial velocity of 0.216 m/s.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Fig. 18. Slip ratio of the experimental conditions as function of the air flow rate, the water flow rate is constant 2500 g s⁻¹. The results are reported within the tube bundle and in the free duct.</figcaption></figure>

flow data presented in Spina et al. (2025) (T1 to T4 corresponding to 0.5 < ṁₐ < 4.0 g s⁻¹ and 0.021 < Jg < 0.168 m s⁻¹ with Jl = 0.126 m s⁻¹).

The comparison depicted in Fig. 17 reveals the inadequacy of the HEM model ($α = \frac{U_{sg}}{U_{sg}+U_{sl}}$) in accurately predicting the void fraction within the tube bundle. On the other hand, the model proposed by Feenstra et al. (2000) (based on a prediction of the velocity ratio of the phases : S = 1 + 25.7 (Ri * Cap)⁰.⁵ (P/D)⁻¹ with Ri and Cap respectively the numbers of Richardson and the Capillary one) serves as a significantly improved approximation; however, its precision diminishes when applied to the intermittent flow regime tests (T5, T6, and T7). This discrepancy may be attributed to variations in the experimental conditions under which the correlation was validated. In their study, Feenstra et al. (2000) employed gamma ray attenuation to obtain an average void fraction measurement within the gap, while in our experiment, we consider the central value of the void fraction within the gap. As a result, the correlation underestimates the void fraction in our setup. Additionally, our experimental conditions are unique due to the large slip ratio (see Fig. 18). Consequently, as the air flow rate in our experiments increases while the water flow rate remains constant, the disparity between Feenstra et al. model and the experimental data becomes more pronounced. This may be because the elevated slip ratio falls outside the validation range for their model. In fact, as reported by Feenstra et al. (2000), their correlation does not consistently perform well for data obtained in an air-water mixture under atmospheric conditions.

The slip ratio (S) is calculated as follows : S = $\frac{P_g}{\rho_l} (\frac{1}{\alpha} - 1)$ in the tube bundle and S = $\frac{U_g}{U_l} (\frac{1}{\alpha} - 1)$ in the duct. The void fraction, denoted as α, is measured using different methods for tube bundle and free duct results. In the tube bundle, it is obtained by the optical probe at point 2 (in the gap of the 3rd row). For tests T1 to T4 in the free duct, it is determined at the tube bundle inlet using the probe at point 5 (data from Spina et al., 2025), while for tests T5 to T7, it is the space-time-averaged void fraction obtained
using the WMS. As observed in Fig. 18, the slip ratio increases with larger air flow rates, reaching values as large as 20 in test T7 in the free duct. The slip ratio upstream the tube bundle is larger than within because of bubble size.

The experimental data collected in this Section, in conjunction with the findings presented in Spina et al. (2025), provide us with the necessary resources to further explore the two-phase flow regimes and their transition boundaries within the TREFLE facility. This, in turn, enables to propose a new flow regime map.

## 5. Two-phase flow regime map

This section presents a proposition for constructing two-phase flow regime maps in tube bundles by incorporating both subjective and objective analyses, combining the strengths of each method to enhance the accuracy and reliability of the predictions.

The data acquired in bubbly flow and the present data can be utilized to propose a methodology for identifying the flow regime and developing a flow regime map specific to the current bundle geometry. Additionally, the analysis of the inlet conditions provides valuable insights into how these conditions influence the flow pattern within the bundle.

Subjective identification of flow regime through visual observations is the most commonly employed method, but it necessitates a predefined definition of the flow regime. Although various definitions have been proposed in the literature, it is crucial to classify the flow regime based on the distinct regimes identified in the present experimental campaign, considering the specific geometry and flow conditions:

* Bubbly flow regime: In the bubbly flow regime, the two-phase flow consists of discrete gas bubbles dispersed within a continuous liquid phase. The gas bubbles are relatively small and uniformly distributed throughout the flow domain. The bubble size is smaller than the gap between the tubes, no gas structures larger than the gap are present.

* Transition regime: The transition regime represents a transitional state between different flow regimes. It occurs when the flow conditions change, causing a shift in the dominant flow behavior. In the context of a tube bundle, the transition regime may occur when there is a change in flow velocity, void fraction, or gas structure sizes. During the transition, the flow characteristics may exhibit a combination of features from multiple flow regimes, making it challenging to categorize the flow into a specific regime.

* Intermittent/Churn flow regime: This regime is characterized by the periodic coexistence of large gas structures and liquid. In this regime, the flow pattern exhibits intermittent variations, with gas or liquid slugs intermittently occupying most of the tube cross-section. The large gas structures can have different lengths and velocities, and their presence causes periodic fluctuations in flow parameters. The gas structures are characterized by a churn motion. The churn motion causes the liquid film to experience intense agitation and disruption. Gas bubbles within the liquid film coalesce and break up, continuously changing the bubble size distribution. This regime is typically unsteady and exhibits complex flow behavior due to the continuous interaction between the liquid and the gas phase. In this scenarios, intermittent and churn flow regimes mix and coexist within the tube bundle.

In order to characterize the flow regime using a subjective methodology, fast camera videos are analyzed, as reported in Spina et al. (2025) and the present work. Additionally, the availability of optical probe measurements allows for a more quantitative approach to identify the flow regime correcting the subjective approach.

A statistical analysis using PDF of void fraction fluctuation was performed to characterize the flow regimes. Statistical analysis employing Probability Density Function (PDF) is widely utilized in the literature. Jones and Zuber (1975) were pioneers in employing a non-visual method based on X-ray measurements of void fraction. They successfully employed PDF analysis to identify various flow regimes such as bubbly, slug, and annular flow in an upward air-water flow within a narrow rectangular channel. The PDF distributions displayed distinctive patterns, with bubbly flow exhibiting a single peak at low void fraction, annular flow showing a single peak at high void fraction, and slug or intermittent flow displaying two peaks representing characteristics of both bubbly and annular flow. Ali (2009) employed PDF analysis of void fraction measured by electrical resistivity probes as an objective approach to identify two-phase flow regimes in circular and narrow channels. Similarly, Noghrehkar et al. (1999) utilized this technique to identify flow regimes in a tube bundle subjected to air-water two-phase flow, successfully identifying bubbly, intermittent, and annular flow regimes. In another study, Aprin et al. (2011) employed optical probe measurements to identify flow regimes across a horizontal tube bundle for three different hydrocarbons under saturated conditions, specifically identifying bubbly and annular dispersed flow regimes.

Before discussing the obtained data, it is valuable to clarify the physical interpretation of the PDF. If we denote the probability that the void fraction $\alpha$ is less than some specific value as $P(\alpha)$, then $\frac{dP(\alpha)}{d\alpha} = p(\alpha)$ would be the probability per unit void fraction that the void fraction ranges between $\alpha$ and $\alpha + d\alpha$. Considering a void-time trace record where the void scale is discretized into equal increments of $\Delta\alpha_i$, and the time scale is partitioned into equal intervals of $\Delta t_j$. If, the void fraction is observed to fall within $\Delta\alpha_i$ a total of $n_i$ times in the total time $T$, and $N$ is the total number of void fraction data registered during $T$, then:

$$ \frac{n_i/N}{\Delta\alpha_i} = \frac{1}{\Delta\alpha_i} \sum_{j=1}^{n_i} \frac{\Delta t_j}{T} \qquad (4) $$

In the case of bubbly flow, a large count ratio $n_i/N$ would be observed at low void fraction values, while smaller ratios would exist in $\Delta\alpha_i$ intervals at higher $\alpha$ values. Conversely, in annular flow, the opposite pattern emerges. Since the ratio $\sum t_j/T$ represents the probability that the void fraction falls within the given interval $\Delta\alpha_i$, we can see that:

$$ \lim_{\Delta\alpha_i \to 0} \frac{1}{T \Delta\alpha_i} \sum_{j=1}^{n_i} \Delta t_j \qquad (5) $$
<figure><img src="image_23.png" /><figcaption>Fig. 19. PDF of void fraction time-evolution to identify the flow regime.</figcaption></figure>

represents the PDF of the specific record under examination. The PDF for this particular record, as given by Eq. (5), will exhibit a distinctive configuration dependent on the nature of the flow passing through the optical probe during the sampling period. Consequently, the outcome of Eq. (5) is expected to produce a low-void peak in the PDF for bubbly flow and a high-void peak for annular-like flow. Conversely, in a churn-like flow, the optical probe may perceive all water with possibly some entrained small bubbles at one instant, yielding a PDF characteristic of bubbly flow. In the next instant, the large gas structure could pass the optical probe, creating a wall film and a center core of gas, resulting in a PDF resembling annular flow. The average is expected to generate a twin-peaked PDF.

In summary, Jones and Zuber (1975) propose that the PDF will exhibit the following behavior:

* "Bubbly-like flows:" A single-peaked PDF at low void fraction.

* "Annular-like flows:" A single-peaked PDF at high void fraction.

* "Churn/Intermittent-like flows:" A twin-peaked PDF, with one peak characteristic of bubbly flow and the other characteristic of annular flow.

In the present work, the optical probe signal from the measurement point 2 (Fig. 1) within the tube bundle was used to perform a PDF analysis of the void fraction time-evolution. As explained before, the void fraction time-evolution ($α(t)$) is calculated using the gas time over a small time window ($T_g(\Delta t)$); hence $α(t) = T_g(\Delta t)/\Delta t$. However, as also reported by Aprin et al. (2011), the PDF shapes are closely related to the windows $\Delta t$. To choose the value of $\Delta t$ that provides the most accurate information about the flow regime, it is necessary to discriminate between large gas structures and small dispersed bubbles.

Within the tube bundle, a “large gas structure” can be defined as a gas structure that overcomes the size of the gap between two tubes (a). Therefore, by obtaining the average gas velocity $v_B$ through the probe itself, the optimal time window for analysis can be determined as $\Delta t = a/v_B$. This approach allows the values of void fraction associated with the large gas structure to be very close to 1, while the gas structures smaller than the gap size are related to the void fraction values from 0.1 to 0.99. The void fraction scale is divided into 20 intervals ($\Delta α_i = 0.05$ as done by Aprin et al., 2011). Fig. 19 shows examples of PDF for bubbly, transition and intermittent flow regimes.

Analyzing Fig. 19, the PDF shapes have a prominent peak around 0 void fraction and show some values for all the void fraction ranges, with the probability that tends to zero for $α > 0.6$, in the bubbly flow regime (Fig. 19(a)). When the regime is in a transition
<figure><img src="image_24.png" /><figcaption>Fig. 20. PSD of void fraction evolution within the tube bundle for flow regime identification, obtained by the optical probe signal.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Fig. 21. Proposed flow regime map, comparison with the literature. The nomenclature according to the authors: B-bubbly, T-transition, I-intermittent, S-slug, C-churn, A-annular, D-dispersed.</figcaption></figure>

zone, some values at 1 start to appear (Fig. 19(b)). Meanwhile, the Intermittent/Churn flow regime shows clear peaks at 0 and 1 with some values within the range of 0.1 to 0.99 (Fig. 19(c)). By analyzing the PSD of the void fraction evolution with respect to the time interval $\Delta t = a/v_B$, the transition between flow regimes can be observed (Fig. 20).

The PSD serves as an indication of the frequency at which large gas structures pass through the tube bundle. Notably, tests T1 to T3 exhibit no low-frequency peaks, suggesting the absence of significant gas structures within the bundle, thus indicating a bubbly flow regime. In contrast, test T4 shows an increase in low-frequency power, implying the presence of some large gas structures traversing the bundle. Tests T5 to T7 clearly demonstrate the excitation of low frequencies, indicating the regular presence of large gas structures traversing the bundle.

It is important to highlight that the PSD presented in Fig. 20 differs from that reported in Fig. 15 due to the selection of different time windows to extract the void fraction time-evolution from the probe signal. Specifically, in Fig. 20, the time windows are chosen to record each gas structure larger than the gap, while in Fig. 15, a smaller time window ($\Delta t = 0.001$ s) allows for the recording of large gas structures smaller than the gap size. To enhance the comprehension of regime boundaries, several additional experiments were conducted alongside tests T1 to T7.

By combining the previously mentioned methods for flow regime classification (visual observation, statistical analysis using PDF, and PSD analysis), a flow regime map for the current bundle geometry and flow mixture is proposed. A sensibility on the $\Delta t$ used for the discretization of the probe signal ($T_g(\Delta t)$) shows no difference for the flow regime identification. The proposed flow regime map can be compared with those presented in the literature for similar bundle geometry and two-phase mixture, as shown in Fig. 21.

The flow regimes boundaries identified in this study differ from those proposed by most other authors. The geometry of the bundle plays a crucial role in determining the flow regime, and the gap between the tubes is a key factor influencing this effect. Performing a sensitivity analysis on the gas injection system for test T4, no substantial difference was reported regarding the flow regime identification. Consequently, different gap sizes could lead to varying evolution of void fraction and gas velocities, which are essential for establishing the flow regime.
<figure><img src="image_26.png" /><figcaption>**Fig. 22.** Tube vibration response spectra (power spectral density) for the different tests T1, T2, T3, T4 from Spina et al. (2025) and T5, T6, T7 according to Table 1 (left). Half power bandwidth for the different tests T1 to T7. In the y-axis is reported the bandwidth where the PSD magnitude correspond to the maximum value divided by the square root of 2 (right).</figcaption></figure>

The present configuration has a gap size of 13.2 mm, while Noghrehkar et al. (1999) used a gap of 5.97 mm. Therefore, even if a similar methodology based on PDF statistical analysis is used, the flow regime boundaries may differ. Ulbrich and Mewes (1994), however, used a gap of 10.0 mm, which is closer to the present configuration. However, their identification method relied mainly on visual observation, which could be misleading as crucial information might not be accessible using fast cameras.

Murakawa et al. (2016) reported the presence of a transition zone similar to the present study, but the regime boundary may differ due to their gap size (7.0 mm). Xu et al. (1998), on the other hand, did not report a transition from the bubbly to churn flow regime for $J_l < 0.2 \ \text{m s}^{-1}$, possibly due to the gap between the tubes being 2.74 mm, and their experimental campaign performed for $J_g > 0.4 \ \text{m s}^{-1}$.

In comparison, there was agreement with the flow regime map from Piteau et al. (2022), as they used a similar method for flow regime identification and had a similar bundle geometry with a gap of 15.0 mm and tube diameter of 30.0 mm. However, Piteau et al. (2022) found a slug flow regime established in the bundle, possibly due to the larger water superficial velocities used in their tests. However, in the test section adopted by Piteau et al. (2022) for flow regime identification, there were only 3 columns of tubes (compared to 5 columns in our present work), resulting in a narrower test section and free duct. It is important to note that the inlet conditions may play a role here, i.e. the slug flow regime is observed only in small diameter pipes.

In conclusion, several factors can affect the flow regime: the bundle geometry, the identification mechanism, the two-phase mixture, and the inlet conditions such as the gas injector and homogenization length. Therefore, the flow regime boundaries should be considered as indications, and each flow regime map is case-dependent.

After conducting a thorough analysis of the two-phase flow, identifying various flow regimes, it is interesting to explore the impact of flow characteristics on tube vibration.

## 6. Tube vibration

Understanding the relationship between flow dynamics and tube vibration is of significant interest and importance. By replacing the central tube in the facility by a vibrating tube equipped with an accelerometer, as described in Spina et al. (2025), it becomes feasible to examine the vibration behavior of the tube subjected to the previously studied two-phase flow. In this section, to complete the analysis, we will reference the tests conducted during the bubbly flow and intermittent flow experimental campaigns, specifically, tests T1, T2, T3, T4 in bubbly flow, and T5, T6, and T7 in intermittent flow, as listed in Table 1. In Fig. 22 are reported the tube acceleration spectra of the different tests.

Similar considerations for the peaks identification can be applied for tests T1 to T7. The vibration modes of the tube correspond to the first peak around 10 Hz (first mode) and the peak around 180 Hz (third mode). By analyzing the first mode of vibration, it can be noted how the peak gains power and becomes broader as the air flow rate increases. The peak power is related to the excitation forces and the amplitude of vibration, both of which increase with the air flow rate. The broadening of the peak can be attributed to the flow regime and the void fraction. In fact, as the void fraction increases and the flow regime acquires an intermittent behavior, the hydrodynamic mass effect is subjected to variations. The continuous changes in the effective mass due to variations in void fraction and intermittent flow behavior cause shifts in natural frequencies and alterations in vibration amplitudes, resulting in broader peaks in the spectrum (as explained also by Moran and Weaver, 2013). Hence, the peak broadening in the tube spectrum can be related to a flow regime transition.

A quantitative approach to estimate the peak broadening is the half power bandwidth (HPB) of the peak corresponding to the first mode of vibration. The bandwidth at half power is the width of the frequency range over which the PSD is greater than or equal to its maximum value divided by the square root of 2. The results are reported in Fig. 22. The impact of the flow regime on the tube vibration response can be appreciated. In fact, the tests in bubbly flow (T1, T2, T3), the test corresponding to a flow regime
<figure><img src="image_27.png" /><figcaption>Fig. 23. PDF of the accelerometer signals for tests T1 to T7 in Fig. 23(a) and its FWHM in Fig. 23(b).</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Fig. 24. RMS of vibration amplitude (left). Normalized two-phase damping comparison between experimental values (calculated according Eq. (7)) and theory according to Pettigrew and Taylor (2003) (Eq. (9)). Both, experimental and calculated values are evaluated using the HEM void fraction model and the measured values of void fraction ($\alpha_m$) (right).</figcaption></figure>

transition (T4), and the tests performed in the intermittent flow regime (T5, T6, T7) can be distinguished, as they are positioned at different levels of bandwidth. More insight on how the flow regime impacts the tube vibration response can be obtained by the PDF of the acceleration data and their full width at half maximum (FWHM), reported in Fig. 23. In this case the FWHM is the width of the acceleration range calculated at half of the maximum PDF value.

Similar behavior is reflected on the root mean square (RMS) plot of the vibration amplitude (Fig. 24). The vibration amplitude is determined by integrating twice the accelerometer signal. As this kind of post treatment might introduce noise, the displacement is verified on few tests to the one recorded by the fast camera (as reported in Spina et al., 2025) to ensure the quality of the results. Here, the amplitude of vibration is of 0.3 to 1.1% of the diameter in bubbly flow (T1 to T4), and of about 3 to 6% in churn flow.

Again, in this case, the impact of the flow regime transition on the vibration amplitude can be observed. Specifically, from test T4 (transition flow regime), the RMS of vibration amplitude start to increase exponentially. The intermittent flow regime induces a significant amplitude of vibration, which could result in the unstable behavior of the tube vibration response. Therefore, based on the analysis conducted so far, it is evident that the transition in flow regime significantly affects the vibration behavior of the tube and that large gas structures are responsible of large fluctuations.

The damping is influenced by the dynamic interactions between the gas and liquid phases, which can vary depending on the predominant flow regime. Damping in two-phase flows plays a crucial role in the stability of tube arrays subjected to instabilities. The interactions between gas and liquid phases lead to energy dissipation, affecting the system ability to sustain vibrations. Accurate determination of damping is challenging but essential for predicting the behavior of tube arrays under various flow conditions. Consequently, design guidelines and predictive models have been developed (Pettigrew and Taylor, 1994). However, measuring damping in two-phase flow poses difficulties, leading to measured values characterized by high uncertainties (Moran and Weaver, 2019). In the open literature the most common and accepted method (Axisa et al., 1990; Nakamura et al., 2002; Pettigrew et al.,
1989a) to measure the damping in two-phase flow ($\zeta_{TP}$) is the one reported by (Carlucci and Brown, 1983):

$$ \zeta_{TP} = \zeta - (\zeta_v + \zeta_f + \zeta_s) \qquad (6) $$

Here $\zeta$ is the measured value of the damping (using the half power method in this case), $\zeta_s$ is the structural damping, and $\zeta_f$ the flow damping, due to the normal component of the fluid drag force on the tube, which is very small in this situation and can be considered negligible in most of the cases (Pettigrew and Taylor, 1994), $\zeta_v$ is the viscous damping calculated according Eq. (7).

$$ \zeta_v = \frac{\pi}{\sqrt{8}} \left( \frac{\rho_{tp} D^2}{m + m_h} \right) \sqrt{\frac{2v_{tp}}{\pi f D^2}} \left\{ \frac{1 + (D/D_e)^3}{[1 - (D/D_e)^2]^2} \right\} \qquad (7) $$

With $m$ the tube mass, $m_h$ the hydrodynamic mass, $v_{tp}$ the two-phase kinematic viscosity (defined as Eq. (8) with $v_l$ and $v_g$ liquid and gas kinematic viscosity), $\rho_{tp}$ the two-phase density (defined as Eq. (8) with $\rho_l$ and $\rho_g$ liquid and gas density), $f$ the natural frequency, $D$ the tube diameter and the ratio $D/D_e$ is defined by Pettigrew and Taylor (1994) as $D/D_e = [(1.07 + 0.56P/D)P/D]^{-1}$ for a square pitch tube bundle.

$$ v_{TP} = v_l(1 - \alpha) + v_g\alpha \quad \text{and} \quad \rho_{TP} = \rho_l(1 - \alpha) + \rho_g\alpha \qquad (8) $$

Following this formulation for the two-phase damping calculation, Pettigrew and Taylor (2003) developed a semi-empirical formulation of damping in two-phase flow (Eq. (9)). The formulation is based on the available database in the literature, with most of the experiments performed in air-water conditions and pitch-to-diameter ratios ranging from 1.22 to 1.47. The expression, take into account the effect of flow regime with a function of the void fraction $f(\alpha)$.

$$ \zeta_{TP} = A \left( \frac{\rho_l D^2}{m + m_h} \right) f(\alpha) \left\{ \frac{1 + (D/D_e)^3}{[1 - (D/D_e)^2]^2} \right\} \qquad (9) $$

In this formulation $A$ is a coefficient determined experimentally ($A = 4$ according to Pettigrew and Taylor (2003)). The value of $f(\alpha)$ take into account the flow regime effect, is estimated to be $\alpha = 0.4$ for $\alpha < 0.4$, $= 1$ for $0.4 < \alpha < 0.7$ and $= 1 - (\alpha - 0.7)/0.3$ for $\alpha > 0.7$ according to Pettigrew and Taylor (2003). Therefore, the measured values of damping in two-phase flow (Eq. (7)) and the semi-empirical formulation (Eq. (9)) can be compared in Fig. 24. To facilitate a comparison between the formula and the experimental values, the HEM void fraction is employed. This is because Eq. (9) is designed to estimate damping without requiring precise knowledge of the exact void fraction values. However, in Fig. 24 the damping values calculated with the measured values of void fraction ($\alpha_m$) are also reported.

The semi-empirical formulation successfully predicts the general trend of two-phase damping. In fact, between tests T1 and T3 (with HEM void fractions of 14% and 40%, respectively), the damping increases. Meanwhile, a change in flow regime occurs at test T4 (57% of HEM void fraction), which corresponds to a decrease in damping as the void fraction increases. However, since the equation serves as a design guideline for steam generators, it is intended to represent a lower bound for damping in two-phase flow. Nonetheless, the damping values obtained for the tests with lower void fractions (T1, T2, and T3) are overestimated by the formula.

Concerning the damping values evaluated with the measured values of void fraction ($\alpha_m$ in Fig. 24), the trend up to test performed with $\alpha_m = 39\%$ is well reproduced (in a conservative way) by the formula provided by Pettigrew and Taylor (2003). However, the measured values of the damping for tests with $\alpha_m > 39\%$ anticipate the decreasing effect due to the intermittent flow regime. This can be attributed to the values of $f(\alpha)$ that were estimated by Pettigrew and Taylor (2003) for the HEM model. Moreover, the experimental damping values (calculated according to Eq. (7)) are slightly smaller when calculated with the measured void fraction compared to the HEM void fraction. This difference becomes more evident as the void fraction increases, indicating that calculating the damping with the HEM model is not a conservative approach.

## 7. Conclusion

A comprehensive analysis of the two-phase flow at the tube bundle inlet and within the tube bundle reveals interesting findings for the intermittent flow regime: large gas structures concentrate in the core of the flow, while small dispersed bubbles occupy the wall region (and the entire section when the slug is not crossing the wire mesh sensor). This void fraction distribution identified with the WMS suggests a weakness in relying only on high-speed cameras, able to visualize only the near wall region. The intermittency of large gas structures is not significantly affected by the presence of the tube bundle, as their frequency remains very similar between the tube bundle inlet and within the bundle. This suggests that the intermittency of this flow regime is not caused by the pressure drop introduced by the tube bundle.

The extensive use of measurement systems provides a database for comparing our data with correlations in the literature to predict void fraction in tube bundle configuration. The homogeneous model for evaluating the void fraction provides very poor estimations, above all in water-air conditions due to the high phase slip velocity. Using specific models for predicting void fraction in tube bundles, such as the one developed by Feenstra et al. (2002), improves the void fraction prediction.

The present work highlights with a local scale characterization of the two-phase flow, the noticeable impact of large gas structure compared to bubbles in the tube vibration response and damping characteristics. The understanding of damping in two-phase flow
<figure><img src="image_29.png" /><figcaption>Fig. 25. Optical probe tip geometric characteristics (left) and optical probe inside the tube bundle.</figcaption></figure>

remains challenging, the gas size distribution appears to play a primary effect. Limited by the gap size, gas structures in churn flow appears to stabilize the damping, as reported in literature. Damping has represents a primary parameter for determining fluid-elastic stability limits: the relations between the two-phase size distribution and the damping need to be investigated in details and offer an interesting perspective for the experimental facility described here.

A flow regime map was proposed, confirming the difficulty to obtain a global agreement among different reported experiments. It is worth noting that variations in bundle geometry and establishment length can significantly influence these results, and the resulting vibration response. Several methods for identifying flow regimes were employed, and a new method based on the frequency of large gas structures was proposed, offering a novel approach to identify the flow regime and study the features of the so-called “intermittent” flow regimes.

The present work represents a major contribution to improve and validate local-scale CFD numerical simulations thanks to its local-scale measurements upstream, inside and downstream of the tube bundle.

### CRediT authorship contribution statement

**Giuseppe Spina:** Writing – review & editing, Writing – original draft, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.
**William Benguigui:** Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.
**Guillaume Bril-lant:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Methodology, Investigation, Formal analysis, Conceptualization.
**Daniele Vivaldi:** Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.
**Catherine Colin:** Writing – review & editing, Validation, Supervision, Methodology, Investigation, Formal analysis.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Appendix

See Figs. 25 and 26.

### Data availability

Data will be made available on request.
<figure><img src="image_30.png" /><figcaption>Fig. 26. Wiremesh geometric characteristics.</figcaption></figure>

References

Ali, S.F., 2009. Two Phase Flow in Large Diameter Vertical Riser (Ph.D. thesis). Departement of Process and Systems Engineering, Cranfield University.

Aprin, L., Tadrist, L., Mercier, P., 2011. Experimental analysis of local void fractions measurements for boiling hydrocarbons in complex geometry. Int. J. Heat Mass Transfer 54, 4203-4219.

Axisa, F., Antunes, J., Villard, B., 1990. Vibration of tube bundles subjected to air-water and steam-water cross flow: Preliminary results on fluidelastic instability. In: ASME Symposium on Flow Induced Vibration. New Orleans, LA.

Axisa, F., Villard, B., Gibert, R.J., Boheas, M.A., 1985. Vibration of tube bundles subjected to steam-water cross flow: A comparative study of square and triangular pitch arrays. In: The 8th International Conference on Structural Mechanics in Reactor Technology. Brussels, Belgium, B1.

Benguigui, W., Benhamadouche, S., Beltran, F., 2024. Experimental and numerical contributions on flow-induced vibration in steam-generator-like tube bundles: A review. Nucl. Eng. Des. 103909.

Benguigui, W., Deri, E., Lavieville, J., Mimouni, S., Longatte, E., 2017. Numerical experiment on two-phase flow behaviors in tube bundle geometry for different mixtures. In: Pressure Vessel & Piping. Hawai, 2017.

Carlucci, L., Brown, J.D., 1983. Experimental studies of damping and hydrodynamic mass of a cylinder in confined two-phase flow. ASME J. Vib. Acoust. Stress. Reliab. Des. 105, 83-89.

Chu, I.C., Chung, H.J., Lee, S., 2011. Flow-induced vibration of nuclear steam generator U-tubes in two-phase flow. Nucl. Eng. Des. 241, 1508-1515.

Connors, Jr., H.J., 1970. Flow-induced vibration of heat-exchangers. J. Mech. Des. ASME 42-56.

De Santis, A., Colombo, M., Hanson, B.C., Fairweather, M., 2021. A generalized multiphase modelling approach for multiscale flows. J. Comput. Phys. 436, 110321.

Delaune, X., Piteau, P., Borsoi, L., Antunes, J., 2018. Experimental investigation of in-flow fluidelastic instability for square tube bundles subjected to single-phase and two-phase transverse flows. In: Proceedings of the 9 International Symposium on Fluid-Structure Interactions, Flow-Sound Interactions, Flow-Induced Vibration and Noise. Toronto, Canada, 2018.

Feenstra, P.A., Weaver, D.S., Judd, R.L., 1995. Fluidelastic instability in a tube array subjected to two-phase R11 cross-flow. J. Fluids Struct. 9, 747-771.

Feenstra, P.A., Weaver, D.S., Judd, R.L., 2000. An improved void fraction model for two-phase cross-flow in horizontal tube bundles. Int. J. Multiph. Flow 26, 1851-1873.

Feenstra, P.A., Weaver, D.S., Judd, R.L., 2002. Modelling two-phase flow-excited damping and fluidelastic instability in tube arrays. J. Fluids Struct. 16, 811-840.

Garnier, J., 1997. Measurement of local flow pattern in boiling R12 simulating PWR conditions with multiple optical probes. In: OECD/CSNI Specialist Meeting on Advanced Instrumentation and Measurements Techniques. Santa Barbara, 17-20.

Grant, I.D.R., Chisholm, D., 1979. Two-phase flow on the shell-side of a segmentally baffled shelland-tube heat exchanger. J. Heat Transf. 10, 38-42.

Hirota, K., Nakamura, T., Kasahara, J., Mureithi, N.W., Kusakabe, T., Takamatsu, H., 2002. Dynamics of an in-line tube array subjected to steam-water cross-flow. Part 3: Fluidelastic instability tests and comparison with theory. J. Fluids Struct. 16, 153-173.

Jones, O.C., Zuber, N., 1975. The interrelation between void fraction fluctuations and flow patterns in two-phase flow. Int. J. Multiph. Flow 2, 273-306.

Kanizawa, F.T., Ribatski, G., Chan, A.M.C., 2016. Two-phase flow patterns across triangular tube bundles for air-water upward flow. Int. J. Multiph. Flow 80, 43-56.

Kataoka, I., Ishii, M., Serizawa, A., 1986. Local formulation and measurements of interfacial area concentration in two-phase flow. J. Multiph. Flow 12, 505-529.

Kiambi, S.L., Duquenne, A.M., Dupont, J.B., Colin, C., Risso, F., Delmas, H., 2003. Measurements of bubble characteristics: Comparison between double optical probe and imaging. Can. J. Chem. Eng. 81, 764-770.

Mao, K., Hibiki, T., 2017. Flow regime transition criteria for upward two-phase cross-flow in horizontal tube bundles. Appl. Therm. Eng. 112, 1533-1546.

Moran, J.E., Weaver, D.S., 2013. On the damping in tube arrays subjected to two-phase cross-flow. J. Press. Vessel. Technol. 135, 1-13.

Moran, J.E., Weaver, D.S., 2019. On modeling fluidelastic instability in tube arrays subjected to two-phase cross-flow. J. Fluids Struct. 90, 1-18.

Murakawa, H., Baba, M., Sugimoto, K., Takenaka, N., Ito, D., Saito, Y., 2016. Evaluation of void fraction around a tube in two-phase flow across horizontal tube bundle. In: 9th International Conference on Multiphase Flow. Firenze, Italy.

Nakamura, T., Fujita, K., Kawanishi, K., Yamaguchi, N., Tsuge, A., 1995a. Study on the vibrational characteristics of a tube array caused by two-phase flow. Part 2: Fluidelastic vibration. J. Fluids Struct. 114, 479-485.

Nakamura, T., Fujita, K., Kawanishi, K., Yamaguchi, N., Tsuge, A., 1995b. Study on the vibrational characteristics of a tube array caused by two-phase flow. Part I: Random vibration. J. Fluids Struct. 9, 519-538.

Nakamura, T., Hirota, K., Watanabe, Y., Mureithi, N.W., Kusakabe, T., Takamatsu, H., 2002. Dynamics of an in-line tube array subjected to steam-water cross-flow. Part 1: Two-phase damping and added mass. J. Fluids Struct. 16, 123-136.

Noghrehkar, G.R., Kawaji, M., Chan, A.M.C., 1999. Investigation of two-phase flow regimes in tube bundles under cross-flow conditions. Int. J. Multiph. Flow 25, 857-874.
Pettigrew, M.J., Taylor, C.E., 1994. Two-phase flow-induced vibration: An overview. J. Press. Vessel. Technol. 116, 233-253.

Pettigrew, M.J., Taylor, C.E., 2003. Ovibration analysis of shell-and-tube heat exchangers: An overview-part 1: Flow, damping, fluidelastic instability. J. Fluids Struct. 18, 469-483.

Pettigrew, M.J., Taylor, C.E., Janzen, V.P., Whan, T., 2002. Vibration behaviour of rotated triangular tube bundles in two-phase cross-flow. J. Press. Vessel. Technol. 124, 144-153.

Pettigrew, M.J., Taylor, C.E., Jong, J.H., Currie, I.G., 1995. Vibration of a tube bundle in two-phase freon cross-flow. J. Press. Vessel. Technol. 117, 321-329.

Pettigrew, M.J., Taylor, C.E., Kim, B.S., 1989a. Vibration of tube bundles in two-phase cross-flow: Part 1 hydrodynamic mass and damping. J. Press. Vessel. Technol. 111, 466-477.

Pettigrew, M.J., Taylor, C.E., Kim, B.S., 1989b. Vibration of tube bundles in two-phase cross-flow: Part 2-fluid-elastic instability. J. Press. Vessel. Technol. 111, 478-487.

Piteau, P., Delaune, X., Panunzio, D., Lagrange, R., Antunes, J., 2022. Experimental investigation of in-flow fluidelastic instability for rotated triangular tube bundles subjected to single-phase and two-phase transverse flows. In: Proceedings of the 12th International Conference on Flow-Induced Vibration. Paris-Saclay, pp. 377-385, 2022.

Prasser, H.M., Bottger, A., Zschau, J., 1998. A new electrode-mesh tomograph for gas-liquid flows. Flow Meas. Instrum. 9, 111-119.

Ricciardi, G., Pettigrew, M.J., Mureithi, N.W., 2011. Fluidelastic instability in a normal triangular tube bundle subjected to air-water cross-flow. J. Press. Vessel. Technol. 133, 1-30.

Sadek, O., Mohany, A., Hassan, M., 2018. Numerical investigation of the cross flow fluidelastic forces of two-phase flow in tube bundle. J. Fluids Struct. 79, 171-186.

Spina, G., Benguigui, W., Brillant, G., Vivaldi, D., Colin, C., 2025. Local-scale experimental investigation of a two-phase cross-flow in a tube bundle and flow-induced vibration; Bubbly flow regime. Nucl. Eng. Des.-

Taitel, Y., Barnea, D., Dukler, A.E., 1980. Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes. AIChE J. 26, 345-354.

Ulbrich, R., Mewes, D., 1994. Vertical, upward gas-liquid two-phase flow across a tube bundle. Int. J. Multiph. Flow 20, 249-272.

Xu, C.P., Tso, G.P., Tou, K.W., 1998. Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle. Int. J. Multiph. Flow 24, 1317-1342.

Zhang, C., 2007. Correlation Between Vibration Excitation Forces and the Dynamic Characteristics of Two-Phase Flow in a Rotated Triangular Tube Bundle (Ph.D. thesis). Departement de genie mecanique ecole polytechnique de Montreal.