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Research Papers: Heat and Mass Transfer

Experimental Investigation of Flow Laminarization in a Graphite Flow Channel at High Pressure and High Temperature PUBLIC ACCESS

[+] Author and Article Information
Francisco I. Valentín

Creare 16 Great Hollow Road,
Hanover, NH 03755
e-mail: fiv@creare.com

Narbeh Artoun

Mem. ASME
City College of New York,
160 Convent Avenue,
New York, NY 10031
e-mail: narbeh.artoun@gmail.com

Masahiro Kawaji

Mem. ASME
City College of New York,
The CUNY Energy Institute,
160 Convent Avenue,
New York, NY 10031
e-mail: mkawaji@ccny.cuny.edu

1Corresponding author.

2Two different definitions are provided for the acronym VHTR.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 18, 2018; final manuscript received June 9, 2018; published online August 3, 2018. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 140(11), 112004 (Aug 03, 2018) (9 pages) Paper No: HT-18-1033; doi: 10.1115/1.4040786 History: Received January 18, 2018; Revised June 09, 2018

Hot wire anemometer (HWA) measurements of turbulent gas flow have been performed in upward forced convection experiments at pressures ranging from 0.6 MPa to 6.3 MPa and fluid temperatures ranging from 293 K to 673 K. The results are relevant to deteriorated turbulent heat transfer (DTHT) and flow laminarization in strongly heated gas flows which could occur in gas-cooled very high temperature reactors (VHTRs).2 The HWA signals were analyzed to directly confirm the occurrence of flow laminarization phenomenon due to strong heating. An X-probe was used to collect radial and axial velocity fluctuation data for pressurized air and pure nitrogen flowing through a circular 16.8 mm diameter flow channel in a 2.7 m long graphite test section for local Reynolds numbers varying from 500 to 22,000. Analyses of the Reynolds stresses and turbulence frequency spectra were carried out and used as indicators of laminar, transition, or fully turbulent flow conditions. Low Reynolds stresses indicated the existence of laminar or transitional flow until the local Reynolds number reached a large value, ∼11,000 to 16,000, much higher than the conventional Re = 4000–5000 for transition to fully turbulent flow encountered in pipe flows. The critical Reynolds number indicating the completion of transition approximately doubled as the pressure was increased from 0.6 MPa to 2.8 MPa.

FIGURES IN THIS ARTICLE
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The study of heat transfer to gaseous coolants at elevated pressures and temperatures has attracted considerable attention due to their high thermodynamic efficiency, chemical inertness, additional safety benefits, and environmental acceptability. Specifically, the U.S. took particular interest in modular very high temperature gas reactor designs (VHTRs) [1], and operated two Gen II gas reactor designs; a prototype helium reactor, Peach Bottom (1967–1974), and a helium-cooled power reactor, Fort Sr. Vrain (1979–1989) [2]. Although both have been decommissioned, much was learned from the operation of these and other gas-cooled reactors worldwide. As part of U.S. Department of Energy's Next Generation Nuclear Plant program and designs proposed for Generation IV reactors, a number of substantial engineering challenges are already expected due to the high temperatures of the coolant involved. Variations of fluid properties along and across heated flow channels in the reactor core are important in VHTRs. The general effects of strong heating include variations of the viscosity and thermal conductivity of the coolant. In addition, a strong reduction of density is expected causing acceleration of the flow in the core due to significant buoyancy forces. A key research area related to the VHTR development is a best-estimate capability to predict coupled conduction–convection heat transfer and calculate the presence of hot spots in the core. In order to develop this capability, it is essential to be able to identify and calculate the flow behavior in the coolant channels and bypass gaps in the reactor core under both operational and accident conditions. In particular, the flow laminarization phenomenon has been intensely investigated since it could give rise to hot spots in the VHTR core [35].

Flow laminarization, also referred to as “deterioration,” “subturbulent,” “reverse transition,” among others, is a phenomenon where flow and convection heat transfer are strongly influenced by the streamwise acceleration, buoyancy, or variation in thermophysical properties [6,7]. It has been proposed that for a turbulent flow in forced convection, the flow acceleration would tend to suppress turbulence bursts from the viscous sublayer and thereby reduce turbulent heat transport [8,9]. Additional influences of rapid flow acceleration on turbulence include increments in viscous shear stress near the wall due to an amplified radial gradient of axial velocity. The turbulence dissipation rate would surpass the turbulence production rate initiating a turbulence decay and reduction in the Reynolds stress [10,11]. These conditions are accompanied by the growth of the thermal boundary layer, which would lead to readjustment of any previously fully developed turbulent velocity profile [12]. The long-term effect of the thermal boundary layer growth is that no truly fully established conditions are reached, because the temperature increments lead to continuous axial and radial variations in thermo-physical properties [13]. Ultimately, a combination of these effects, including temperature variations and substantial reductions in turbulent kinetic energy may cause the turbulent flow to laminarize, leading to lower heat transfer coefficients than expected due to decreases in turbulent heat transport [1418].

Significant differences and uncertainties have been found among heat transfer correlations for these conditions [19]. Improved computational techniques and supporting measurements are needed to assist the developers of reactor design and safety analysis codes to treat the property variations and their effects reliably for some operating conditions and hypothetical accident scenarios. The geometries of the coolant flow channels in the core including bypass flow channels are also an issue since most of these geometries are more complex than those that have been used to generate the empirical heat transfer correlations employed in the thermal hydraulic codes. Advanced computational techniques may be applied but measurements with realistic geometries close to actual operating conditions (pressure and temperature) are needed to assess the reliability and accuracy of their predictions.

Therefore, measurements of the turbulence quantities are necessary to assess direct numerical simulation and large eddy simulation codes for application to intensely heated gas flows with heat transfer. To further support the existence of the flow laminarization phenomenon, turbulence measurements have been performed using a high temperature hot wire anemometer (HWA) in the experimental facility described Valentín et al. [20] under high pressure and high temperature conditions. Through the use of this instrumentation, quantitative measurements of turbulence parameters were performed. A richer understanding of the impact of flow laminarization on turbulence parameters was explored leading to a clearer understanding and identification of critical transitional Reynolds number values.

Hot wire anemometry is a well-established technique to carry out velocity and turbulence measurements. Hot wire anemometer measurements in this work were performed using constant temperature anemometry (CTA), whose operational principle is a rather simple one; the thermal loss of a heated sensor (the HWA probe wire) is correlated to the magnitude of convective heat loss which is dependent on velocity. Very small wires (∼5 μm) are heated to maintain a constant temperature, by adjusting the electric current flowing through the wires. Hot wire anemometry assumes that convective heat transfer is the only form of heat transport from the heated sensor; thus an energy balance can be carried out between the known input power (I2R) and convective heat loss through Newton's law of cooling. Under this assumption, heat loss is a function of the local fluid temperature, pressure, and velocity. If all variables except for the fluid velocity are kept constant, then the magnitude of convective heat loss can be directly related to the fluid velocity [21].

The HWA probe measurements were essential for the detection of laminarization of flow under intense heating conditions in previous studies [22]. Shehata [23] reported the local distributions of velocity and temperature for turbulent forced air flows in a vertical circular tube. Their measurements were carried out under strong heating conditions covering flows ranging from turbulent to laminar [23]. Their data have been used for code validation purposes, for example, by Satake et al. [14].

Recently, evidences of flow laminarization have been experimentally obtained at City College of New York by conducting high temperature forced convection experiments and measuring the impact of high heat fluxes on heat transfer parameters [20,2426]. These papers have provided: (1) validation of the methodology and data reduction techniques by directly comparing nondimensional hydraulic parameters to popular turbulent flow correlations, and (2) evidence of the impact of acceleration, buoyancy, and property variation due to strong heating, on both heat transfer enhancement and deterioration of strongly heated gases through the calculation of local heat transfer parameters. This work presents further advances in understanding of the turbulence structure, the identification, and validation of flow laminarization which is of importance for forced convection heat transfer in graphite channels of a very high temperature gas cooled reactor with a prismatic core, as well the conditions of deteriorated heat transfer for supercritical water in fossil fuel fired boilers and nuclear reactors. In particular, this work elucidates the influence of pressure on delayed transition between laminar and turbulent flow. Currently, there exists no such measurements of turbulence quantities, in the pressure ranges described in this work [25,26]. Thus, the thermal-hydraulic data obtained could be used for the development of VHTR design codes and safety analysis codes in coordination with other U.S. Department of Energy projects underway or being planned within the Next Generation Nuclear Plant experimental verification and validation (V&V) program.

This work presents turbulence data for air and nitrogen flows obtained using a HWA system. The use of air and nitrogen as experimental fluids allowed a wide range of inlet Reynolds numbers to be investigated compared with much lighter gases such as helium. The present data expands the current flow laminarization database by covering gas temperatures up to 673 K at pressures ranging from 0.6 to 6.3 MPa. By describing the data through the use of dimensionless quantities, the data will also be useful for model validation especially for the development of very high temperature reactors. In addition, the present hot wire anemometer data provide both evidence for the occurrence and a better understanding of flow laminarization, and its impact on turbulence quantities.

Flow laminarization has been closely related to deteriorated turbulent heat transfer (DTHT). As such, dimensionless quantities describing flow acceleration and buoyancy parameters have been defined representing the threshold for the likely occurrence of laminarizaiton [6,7]. DTHT regimes have also been identified when the local heat transfer coefficients are at least 20% below the expected values based on popular turbulent flow correlations [27]. In addition, reductions in the Reynolds stress have been observed although laminarization thresholds based on this parameter have not been defined [10]. By measuring velocity fluctuations for varying wall heat fluxes, this work could lead to either a confirmation or modification of flow laminarization criteria.

A schematic of the gas flow loop used in experiments involving air is shown in Fig. 1(a). Compressed air entered the test section from an air compressor, and heated in a 2.7 m long graphite test section. The air was then cooled through a water-cooled heat exchanger and discharged to the ambient. Experiments involving nitrogen gas were performed in a closed flow loop equipped with two booster pumps operating in parallel and high and low pressure gas cylinders to circulate the gas through the test section continuously [20]. Closed loop experiments were limited to lower inlet Reynolds numbers than the tests involving air compressor operations.

The test section consisted of a stainless steel pressure vessel (ASME certified at 6.9 MPa/623K) containing a graphite (G348) test section with a 16.8 mm diameter, 2.7 m long flow channel at the center. A schematic of the test section is shown in Fig. 1(b). Additional details can be found in Valentín et al. [20,2426]

Turbulence measurements were made using a custom-made HWA X-probe for use at high temperatures (up to 750 °C). It was fabricated by Dantec Dynamics based on their 55P61 probe design, which is capable of detecting gas velocities between 0.05 m/s and over 100 m/s. The hot wire anemometer probe was inserted vertically into the coolant channel of the test section and connected to two channel CTA units [54T42, Dantec Dynamics] which provided velocity data in axial and transverse directions, u and v, respectively. A data reduction analysis which will be discussed later in this section, allowed for calculations of velocity fluctuations, turbulence intensity and Reynolds shear stress.

An image of the hot-wire sensor experiment setup is shown in Fig. 2. As can be seen, the sensor was placed slightly off-center in the flow channel. This was done intentionally to capture velocity fluctuations and turbulence measurements near the wall, where their magnitudes should be higher than near the centerline. A 1.6 mm diameter (1/16 in) type-k thermocouple was also placed 2.54 cm (1 in) downstream of the hot-wire probe. Its temperature reading was used for velocity correction and fluid temperature monitoring purposes.

The experimental methodology was as follows: (i) a desired bulk temperature at the test section exit was selected ranging up to 673 K, (ii) a test pressure was selected from 0.68, 1.70, or 2.72 MPa for air and 3.4, 4.76, and 6.12 MPa for nitrogen, (iii) the heater power was increased for a given flow rate, increasing the graphite wall temperature until the fluid at the exit achieved the desired temperature, and (iv) the flow rate was increased to a desired value and the procedure was repeated.

Calibration Procedure.

Figure 3 displays an example of the transient volumetric flow rate data collected at a rate of 1.0 Hz during both calibration and data acquisition periods. The hot wire anemometer probe was sampled at 10 kHz for various flow regimes. For calibration purposes, a fifth-order polynomial relating the fluid velocity to a corrected HWA output voltage was obtained by applying temperature correction factors. In order to perform temperature corrections and to facilitate processing of HWA signals, a thin thermocouple probe was attached to the high temperature hot wire anemometer probe as previously shown in Fig. 2.

For velocity calibration purposes, a mass flow meter installed downstream of the test section was then used to calibrate the HWA measurements of velocities after applying density and flow area corrections. Both pressure and temperature were measured in the test section near the hot-wire probe, which were then used for density and velocity calculations using the conservation of mass principle as given by Eqs. (1)(3). Ten velocities were then used to produce a calibration curve which was then used for the measurement of turbulence intensities Display Formula

(1)m˙=ρU¯A
Display Formula
(2)ρ=ρ(T,p)
Display Formula
(3)Ui=C0+C1Ecorr+C2Ecorr2+C3Ecorr3+C4Ecorr4+C5Ecorr5

Here, C0 through C5 are calibration constants.

Due to the off-center location of the hot wire probe, an assumption was made to consider the local velocity and temperature measured at the hot wire probe location as representative of the bulk velocity and temperature, respectively. Future uncertainty estimates will quantify the approximate error due to this assumption.

Data Conversion Procedure.

This section describes the data conversion procedure once the hot wire probe data were obtained at a sampling rate of 10 kHz. A total of N = 100,000 samples were recorded for every sampling of the flow. The preliminary data were analyzed in order to determine the appropriate sampling rate and sampling periods. The chosen values proved to be close to ten times the main frequency component of turbulence; making 10 kHz a sufficiently high sampling rate.

Once the velocity–voltage calibration curve was obtained, tests were continued by sampling the flow at velocities within the calibration range while maintaining a close-to-constant fluid temperature at the hot wire probe. Three different stages can be seen in the mass flow rate behavior during a particular hot wire calibration test as shown earlier in Fig. 3: (a) initial heating period where the graphite temperature increased; (b) calibration stage where the voltage–velocity calibration curve and polynomial are generated; (c) a period where the flow rate is modified, which in turn modifies the velocity measured by the hot wire probe in order to obtain velocity fluctuations at different flow velocities. The mass flow rate was chosen in such a way as to obtain approximately 12 sets of data for the local Reynolds number varying from ∼1000 to ∼22,000.

During the testing period, the HWA was operated in a CTA mode, and the fluid temperature (Ta) was acquired along with the miniCTA voltage (Ea). The miniCTA voltage was then corrected according to Display Formula

(4)Ecorr=(TwT0TwTa)0.5Ea

where Tw is the sensor hot temperature which is found as: a/a0 + T0. The variables, a, a0, and T0, refer to an overheat ratio, sensor temperature coefficient at ambient reference temperature, and ambient reference temperature, respectively. This expression is acceptable as long as the condition, T0 −5% < Ta < T0 + 5%, is satisfied [28].

Following the calculation of the corrected voltage from Eq. (4), the velocity from each sensor, Ui, was calculated according to Eq. (3). Using the two velocities from the two sensors, the axial and transverse velocity components, U and V, were calculated using Eqs. (5) and (6)Display Formula

(5)U=22U1+22U2
Display Formula
(6)V=22U1+22U2

From the two velocity components and by using Eq. (7) through Eq. (10), the mean velocity, standard deviation of instantaneous velocity, turbulence intensity, and Reynolds stress were calculated as follows: Display Formula

(7)Umean=1N1NUi
Display Formula
(8)Urms=(1N11N((UiUmean)2))0.5
Display Formula
(9)Tu=UrmsUmean
Display Formula
(10)uv¯=1Ni=1NUiUmean·ViVmean

Experimental Uncertainties.

The uncertainty in the velocity measurement from each HWA sensor was calculated from the following equation [28]: Display Formula

(11)ε(Usample)=i=1N(1k1UsampleΔyi)22

where ε, k, and Usample represent uncertainty, measured velocity, and the coverage factor describing the error distribution (Gaussian, rectangular, etc.) of each output variable yi. Equation (12) takes into account the following uncertainty sources: (a) calibration equipment, (b) linearization uncertainty related to curve fitting errors, (c) A/D board resolution, (d) probe positioning, (e) temperature variations, (f) ambient pressure variations, and (g) gas composition changes due to changes in relative humidity. The relative expanded uncertainty in hot wire velocity measurements was estimated to be 5.4% for both sensors. The uncertainty was a strong function of the linearization error while calibration curves generated a typical error of 2%. Uncertainties in the measured fluid temperature, pressure, mass flow rate, and Reynolds number were: 1.1%, 0.5%, 1.1%, and 5.5%, respectively.

Effect of Temperature on Turbulence Intensity.

Figure 4 shows variations of the ratio of local graphite wall temperature to local fluid temperature with the local Reynolds number for local air and nitrogen temperatures of 473 K and 673 K, respectively, at the HWA probe location. The local Reynolds number was calculated with the air and nitrogen densities and viscosities evaluated at the local fluid temperature. As the gas flow rate is increased, the graphite wall temperature keeps increasing at low Reynolds numbers, indicating laminar convection and low convection heat transfer coefficient. A sudden drop in the wall-to-fluid temperature ratio occurs after reaching a peak, as the laminar/transition convection changes to a fully turbulent flow, and the convection heat transfer coefficient increases significantly.

As can be observed, the peak graphite wall-to-fluid temperature ratio occurred at higher Reynolds numbers than the conventional Reynolds number of ∼4000, at which the flow transitions to fully turbulent flows. So, the present data for the critical Reynolds number, Recomp, marking the completion of the transition indicate Recomp > 5000 [29]. A delay in completion of flow transition is observed to be a strong function of pressure. These observations are consistent at low pressures (Fig. 4(a)) and at higher pressures (Fig. 4(b)). From the trend displayed in Fig. 4(a), it could be hypothesized, for example, that at a local fluid temperature of 473 K and ambient pressure, air flows would complete transition at a local Reynolds number close to 4200 which would be consistent with conventional turbulent flow theory.

Experiments were extended and conducted with nitrogen gas at local fluid temperatures up to 673 K and maximum pressures of 6.12 MPa. Figure 5(a) displays the graphite wall-to-fluid temperature ratio for three different exit bulk temperatures. General conclusions that can be drawn from these experiments are presented in Fig. 5(b), which shows the Reynolds number corresponding to the peak graphite-to-fluid temperature ratio. The results displayed in Fig. 5(b) were all at local fluid temperatures of 473 K. A very strong relation is seen to exist between pressure and the Reynolds number corresponding to the maximum graphite-to-fluid temperature ratio. However, no significant dependency between this ratio and temperature has been found at a given pressure.

It is the authors belief that the graphite wall-to-fluid temperature ratio can be used as an indirect indicator of heat flux and heat transfer coefficient. Once the maximum graphite wall-to-fluid temperature has been reached, this could signal the end of the DTHT regime. Following the end of the DTHT regime the flow will eventually complete its transition into fully turbulent flow. Analyses complementing these hypothesis will be presented in the Temperature/Shear Analogy and Completion of Transition to Fully Turbulent Flow section. Another relevant conclusion that can be obtained by observing the results from Figs. 5 and 6, is that the temperature influences the rate increase in the graphite-to-fluid temperature ratio. For a given Reynolds number range, as the fluid temperature increases, the ratio of wall temperature to fluid temperature must also increase to maitain a constant fluid temperature. This would suggest that the impact of fluid temperature on convective heat transfer, i.e., the rate at which heat transfer is degradated, increases with fluid temperature.

Temperature/Shear Analogy and Completion of Transition to Fully Turbulent Flow.

No clear trends have been observed regarding the impact of strong heating on the axial velocity fluctuations. However, interesting fluid behavior characteristics have been detected in the rms of radial velocity fluctuations, vrms. This could give further evidence of flow laminarization and also provide insight into the physical behavior of the flow to better understand this phenomenon. Figure 6 shows the turbulence intensity of the radial velocity component as a function of local Reynolds number for two pressures and three local fluid temperatures. As can be observed, increasing the operating temperature by 60% from 293 K to 473 K decreased the turbulence intensity by 50% at 2.72 MPa and close to 75% at 1.70 MPa.

Conjugate heat transfer and turbulent mixing is essentially dominated by radial velocity fluctuations; which, as evident from Fig. 6, is a strong function of the local gas temperature. In addition, the present results highlight the anisotropic nature of these turbulent flows. For flows with Reynolds numbers above 2300, and temperatures of at least 373 K, radial and axial velocity fluctuations differed by at least 60%. Information of this type is relevant and essential to turbulence modeling. Turbulence models, such as the kε model, rely on certain principles and assumptions, such as isotropic turbulence, for example.

To further confirm the completion of transition of transitional flows to fully turbulent at Reynolds numbers well above 4000 in strongly heated flows, the Reynolds stress, uv¯, evaluated from measured turbulence fluctuations, u′ and v′, is shown (triangles) against the local Reynolds number, along with the graphite wall-to-fluid temperature ratio (circles) in Fig. 7. The variations in the Reynolds stress and wall-to-fluid temperature ratio shown in Fig. 7 confirm the existence of transitional flow up to the local Reynolds number of ∼11,000 to 16,000, below which the Reynolds stress is significantly lower than those in the fully turbulent flow regime.

Figure 7 also displays the existence and range of the deteriorated turbulent heat transfer flow regime, marked as (DTHT) in the figure. The same range is also marked in the figures as the range of laminarized flows. These regions are characterized by lower heat transfer rates than expected for turbulent flows. The end of the DTHT is then marked by the highest wall-to-fluid temperature ratios followed by a sharp drop resulting in an equal local fluid temperature for particular test conditions. After the maximum Twall/Tfluid, is reached, turbulent heat transport enhances the convection heat transfer and lowers the graphite wall temperature significantly. Since the inlet Reynolds number was considerably higher (Rein > 1.3ReHWA)3 than that at the HWA location because of the much lower bulk temperature, greater density, and lower viscosity at the inlet, the flow may have remained laminar at even higher Reynolds numbers than the transition Reynolds numbers indicated in Fig. 7. To our knowledge, the present data are the first to experimentally confirm the laminarization phenomenon in a high pressure gas flow due to strong heating.

Energy Spectrum Analysis.

This section complements the previous analysis of the HWA data, by performing a frequency spectrum analysis on the HWA signals. One of the advantages of frequency spectrum analyses is the ease of finding evidence of flow laminarization since the frequency spectrum analysis does not require the user to generate a velocity/voltage calibration curve. Figure 8 displays an example of the raw hot-wire anemometer signal for air at 2.72 MPa at 293 K. A total of 100,000 samples were collected at 10 kHz. The mean voltage value was subtracted from the acquired voltage.

A Butterworth high pass filter was applied, with a cutoff frequency of 20 Hz. This was done in order to separate the turbulence component from the signal describing the mean velocity component. Figure 9 displays the raw signal and modified signal after applying the high-pass filter. The turbulence information is assumed to be given by the difference between the raw signal and the processed signal after applying the high pass filter. These are shown in Fig. 9 for sensors 1 and 2.

After the voltage signal describing the flow turbulence was obtained, a fast-Fourier transform (FFT) analysis was performed, on the raw signal and the signal describing the fluid turbulence. The power spectra are shown in Fig. 10 for sensors 1 and 2. In order to elucidate the effects of pressure and temperature on the frequency components, the following analysis was carried out. The magnitude of the FFT amplitude was squared and summed over the entire frequency spectrum as given by Eq. (12). This would provide one sum (S) for a given experiment. This procedure is used to calculate the energy carried by the waveform. Display Formula

(12)Sk=i=1i=NFFTi2

Figure 11 displays the results of two air flow experiments at 1.70 and 2.72 MPa. A very strong correlation is found between the Reynolds stress and the sum of FFT2. At nearly the same local Re, both the Reynolds stress and sum of FFT2 show a sharp increase. Thus, the end of flow laminarization can be detected from the frequency spectra of the HWA signal, and the corresponding Reynolds number could be determined from a combination of mass flow and temperatures measurements, which do not require rigorous calibration procedures. Further experiments will provide additional support for this approach. Another interesting observation is that nonheated tests display a nearly linear variation of the sum of FFT2 (see Fig. 12) with local Reynolds number, unlike those displayed in Fig. 11 which clearly shows the effects of flow transition. Strong heating seems to modify the linearity, causing the appearance of transition regions.

Hot wire anemometer measurements of turbulence fluctuations in upward forced convection experiments were performed and analyzed to directly confirm the flow laminarization phenomenon due to strong heating. Air and nitrogen flows were tested at pressures up to 2.8 MPa for air and between 3.4 and 6.3 MPa for nitrogen, and the fluid temperature near the exit ranged up to 493 K for both gases. An X-probe was used to collect radial and axial velocity fluctuation data for pressurized gases flowing through a circular 16.8 mm diameter flow channel in a 2.7 m long graphite test section for local Reynolds numbers varying from 500 to 22,000. The results are reported for quasi-steady-state tests, where the heater power and wall temperature were varied to maintain a constant fluid temperature, Tf,HWA, at the HWA probe location for different flow rates at a given pressure. Experimental data showed:

  • Laminar convection persisted until Reynolds numbers well above the critical Reynolds number of about 2300 indicating the complete transition from laminar flow at Recomp = 4000–5000.

  • A drop in the wall temperature occurred after reaching a peak value, as flow conditions reached the end of DTHT regime and the convection heat transfer coefficient increased significantly due to an increase in the turbulent heat transport.

  • The end of the DTHT regime, as indicated by the graphite wall temperature data, occurred at local Reynolds numbers varying from 6000 to 16000, depending on the local pressure; approximately doubling as the pressure was increased from 0.6 to 2.8 MPa.

Analyses of the Reynolds stress, uv¯, evaluated from measured velocity fluctuations and turbulence frequency spectra were carried out and used as indicators of laminar, transition, and fully turbulent flow conditions. The results showed the following.

  • Low Reynolds stresses indicated the existence of laminar or transitional flow until the local Reynolds number reached a large value, ∼11,000–16,000.

  • A transition to fully turbulent flow was marked by a sudden and sharp increase in the Reynolds stress, dominated by the radial velocity fluctuations which were observed to be most affected by pressure and temperature.

  • The transition to fully turbulent flow was marked by an increase in the total energy carried by the waveform as revealed by the frequency spectrum analysis.

Since the inlet Reynolds number was considerably higher than that at the HWA location due to a significantly lower inlet bulk temperature and higher density and lower viscosity, the flow may have remained laminar at Reynolds numbers much higher than the commonly accepted transition flow Reynolds numbers of ∼4000. To our knowledge, the present data are the first to directly confirm the occurrence of a flow laminarization phenomenon in a high pressure gas flow due to strong heating. Thus, in the operation of VHTRs at high pressures, strong heating in the prismatic reactor core could induce laminar convection although the Reynolds numbers could be well above the conventional critical Reynolds number of ∼2300.

The authors would like to thank Professor Y. Andreopoulos and Dr. Vahid Azadeh-Ranjbar for their assistance in performing hot-wire anemometer calibration and data reduction and analysis. This work has been supported by a grant from the U.S. Department of Energy's Nuclear Energy University Program under Contract No. DE-AC07-05ID14517.

  • Office of Nuclear Energy (DE-AC07-05ID14517).

  • E =

    voltage (V)

  • Ea =

    acquired voltage (V)

  • Ecorr =

    corrected voltage (V)

  • I =

    sensor current (amp)

  • m˙ =

    mass flow rate (kg/s)

  • N =

    number of samples

  • R =

    sensor resistance (ohm)

  • Re =

    Reynolds number

  • T =

    temperature (K)

  • Ta =

    ambient temperature (K)

  • T0 =

    reference temperature (K)

  • Tu =

    turbulence intensity

  • Tw =

    sensor temperature (K)

  • U =

    axial velocity (m/s)

  • uv =

    Reynolds stress (N/m2)

  • V =

    transverse velocity (m/s)

  • ρ =

    fluid density (kg/m3)

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McEligot, D. M. , Chu, X. , Skifton, R. S. , and Laurien, E. , 2017, “ Internal Convective Heat Transfer to Gases in the Low-Reynolds-Number ‘Turbulent’ Range,” Int. J. Heat Mass Transfer, 121, pp. 1118–1124. [CrossRef]
Mikielewicz, D. P. , Shehata, A. M. , Jackson, J. D. , and McEligot, D. M. , 2002, “ Temperature, Velocity and Mean Turbulence Structure in Strongly Heated Internal Gas Flows. Comparison of Numerical Prediction With Data,” Int. J. Heat Mass Transfer, 45(21), pp. 4333–4352. [CrossRef]
Satake, S. I. , Kunugi, T. , Shehata, A. M. , and McEligot, D. M. , 2000, “ Direct Numerical Simulation for Laminarization of Turbulent Forced Gas Flows in Circular Tubes With Strong Heating,” Int. J. Fluid Flow, 21(5), pp. 526–534. [CrossRef]
Bankston, C. A. , 1970, “ The Transition From Turbulent to Laminar Gas Flow in a Heated Pipe,” Trans. ASME. Ser. C, 92(4), pp. 569–579. [CrossRef]
McEligot, D. M. , Coon, C. M. , and Perkins, H. C. , 1970, “ Relaminarization in Tubes,” Int. J. Heat Mass Transfer, 13(2), pp. 431–433. [CrossRef]
Ogawa, M. , Kawamura, H. , Takizuka, T. , and Akino, H. , 1982, “ Experiment on Laminarizaticn of Strongly Heated Gas Flow in Vertical Circular Tube,” J. At. Energy Soc. Jpn., 24, pp. 60–67 (in Japanese). [CrossRef]
Shehata, A. M. , and McEligot, D. M. , 1998, “ Mean Structure in the Viscous Layer of Strongly Heated Internal Gas Flows: Measurements,” Int. J. Heat Mass Transfer, 41(24), pp. 4297–4313. [CrossRef]
Nishimura, M. , Fujii, S. , Shehata, A. M. , Kunugi, T. , and McEligot, D. M. , 2000, “ Prediction of Forced Gas Flows in Circular Tubes at High Heat Fluxes,” J. Nuc. Sci. Technol., 37(7), pp. 581–594. [CrossRef]
Valentin, F. I. , Anderson, R. , and Kawaji, M. , 2017, “ Experimental Investigation of Convection Heat Transfer in High Pressure and High Temperature Gas Flows,” ASME J. Heat Transfer, 139(9), p. 091704. [CrossRef]
Bruun, H. H. , 1996, Hot-Wire Anemometry: Principles and Signal Analysis, Oxford University Press, Oxford, UK.
McEligot, D. M. , and Bankston, C. A. , 1969, “ Numerical Predictions for Circular Tube Laminarization by Heating,” ASME Paper No. 69-HT-52.
Shehata, A. M. , 1984, “ Mean Turbulence Structure in Strongly Heated Air Flows,” Ph.D. thesis, University of Arizona, Tucson, AZ. https://repository.arizona.edu/handle/10150/187902
Valentín, F. I. , 2016, “Experimental and Numerical Investigations of High Temperature Gas Heat Transfer and Flow in a VHTR Reactor Core,” Ph.D. thesis, Department of Mechanical Engineering, City College of New York, New York. http://adsabs.harvard.edu/abs/2016PhDT........40V
Valentín, F. I. , Artoun, N. , Kawaji, M. , and McEligot, D. M. , 2018, “ Forced and Mixed Convection Heat Transfer at High Pressure and High Temperature in a Graphite Flow Channel,” ASME J. Heat Transfer (epub).
Valentín, F. I. , Artoun, N. , Anderson, R. , Kawaji, M. , and McEligot, D. M. , 2017, “ Study of Convection Heat Transfer in a VHTR Flow Channel: Numerical and Experimental Results,” Nucl. Technol., 196(3), pp. 661–673. [CrossRef]
Lee, J. I. , Hejzlar, P. , Saha, P. , Kazimi, M. S. , and McEligot, D. M. , 2008, “ Deteriorated Turbulent Heat Transfer (DTHT) of Gas Up-Flow in a Circular Tube: Experimental Data,” Int. J. Heat Mass Transfer, 51(21–22), pp. 3259–3266. [CrossRef]
Jørgensen, F. E. , 2002, “ How to Measure Turbulence With Hot-Wire Anemometers: A Basic Guide,” Dantec Dynamics, Skovlunde, Denmark.
Kakac, S. , Shah, R. K. , and Aung, W. , 1987, Handbook of Single-Phase Convective Heat Transfer, Wiley, Hoboken, NJ.
Copyright © 2018 by ASME
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References

Kadak, A. C. , 2016, “ The Status of the U.S. High-Temperature Gas Reactors,” Engineering, 2(1), pp. 119–123. [CrossRef]
Copinger, D. A. , and Moses, D. L. , 2004, “ Fort Saint Vrain Gas Cooled Reactor Operational Experience,” Division of Systems Analysis and Regulatory Effectiveness, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, Washington, DC, Technical Report No. ORNL/TM-2003/223. https://www.nrc.gov/docs/ML0403/ML040340070.pdf
Vilim, R. B. , Pointer, W. D. , and Wei, T. Y. C. , 2006, “ Prioritization of VHTR System Modeling Needs Based on Phenomena Identification, Ranking and Sensitivity Studies,” Nuclear Engineering Division, Argonne National Laboratory, Lemont, IL, Technical Report No. ANL-GenIV-071. http://www.ipd.anl.gov/anlpubs/2007/08/59659.pdf
Ball, S. J. , and Fisher, S. E. , 2007, “ Next-Generation Nuclear Plant (NGNP) Phenomena Identification and Ranking Table (PIRT) for Accident and Thermal Fluids Analysis,” Main Report, Oak Ridge National Laboratory, Oak Ridge, TN, Technical Report No. NUREG/CR-6944.
Schultz, R. R. , Bayless, P. D. , Johnson, R. W. , McCreery, G. E. , Taitano, W. , and Wolf, J. R. , 2010, “ Studies Related to the Oregon State University High Temperature Test Facility: Scaling, the Validation Matrix, and Similarities to the Modular High Temperature Gas-Cooled Reactor,” Idaho National Laboratory, Idaho Falls, ID, Technical Report No. INL/EXT-10-19803.
McEligot, D. M. , 1986, “ Convective Heat Transfer in Internal Gas Flows With Temperature-Dependent Properties,” In A. S. Majumdar and R. A. Mashelkar (eds.). Advances in Transport Processes, Vol. IV, pp. 113–200. Wiley, New York.
Hall, W. B. , and Jackson, J. D. , 1969, “ Laminarization of a Turbulent Pipe Flow by Buoyancy Forces,” ASME Paper No. 69-HT-55.
Corino, E. R. , and Brodkey, R. S. , 1969, “ A Visual Observation of the Wall Region in Turbulent Flow,” J. Fluid Mech., 37(01), pp. 1–30. [CrossRef]
McEligot, D. M. , and Jackson, D. J. , 2004, “ Deterioration Criteria for Convective Heat Transfer in Gas Flow Through Non-Circular Ducts,” Nucl. Eng. Des., 232(3), pp. 327–333. [CrossRef]
Gordeev, S. , Heinzel, V. , and Slobodtchouk, V. , 2005, “ Features of Convective Heat Transfer in Heated Helium Channel Flow,” Int. J. Heat Mass Transfer, 48(16), pp. 3363–3380. [CrossRef]
Launder, B. E. , 1964, “ Laminarization of the Turbulent Boundary Layer by Acceleration,” MIT Gas Turbine Lab, Cambridge, MA, Technical Report No. 77.
McEligot, D. M. , Chu, X. , Skifton, R. S. , and Laurien, E. , 2017, “ Internal Convective Heat Transfer to Gases in the Low-Reynolds-Number ‘Turbulent’ Range,” Int. J. Heat Mass Transfer, 121, pp. 1118–1124. [CrossRef]
Mikielewicz, D. P. , Shehata, A. M. , Jackson, J. D. , and McEligot, D. M. , 2002, “ Temperature, Velocity and Mean Turbulence Structure in Strongly Heated Internal Gas Flows. Comparison of Numerical Prediction With Data,” Int. J. Heat Mass Transfer, 45(21), pp. 4333–4352. [CrossRef]
Satake, S. I. , Kunugi, T. , Shehata, A. M. , and McEligot, D. M. , 2000, “ Direct Numerical Simulation for Laminarization of Turbulent Forced Gas Flows in Circular Tubes With Strong Heating,” Int. J. Fluid Flow, 21(5), pp. 526–534. [CrossRef]
Bankston, C. A. , 1970, “ The Transition From Turbulent to Laminar Gas Flow in a Heated Pipe,” Trans. ASME. Ser. C, 92(4), pp. 569–579. [CrossRef]
McEligot, D. M. , Coon, C. M. , and Perkins, H. C. , 1970, “ Relaminarization in Tubes,” Int. J. Heat Mass Transfer, 13(2), pp. 431–433. [CrossRef]
Ogawa, M. , Kawamura, H. , Takizuka, T. , and Akino, H. , 1982, “ Experiment on Laminarizaticn of Strongly Heated Gas Flow in Vertical Circular Tube,” J. At. Energy Soc. Jpn., 24, pp. 60–67 (in Japanese). [CrossRef]
Shehata, A. M. , and McEligot, D. M. , 1998, “ Mean Structure in the Viscous Layer of Strongly Heated Internal Gas Flows: Measurements,” Int. J. Heat Mass Transfer, 41(24), pp. 4297–4313. [CrossRef]
Nishimura, M. , Fujii, S. , Shehata, A. M. , Kunugi, T. , and McEligot, D. M. , 2000, “ Prediction of Forced Gas Flows in Circular Tubes at High Heat Fluxes,” J. Nuc. Sci. Technol., 37(7), pp. 581–594. [CrossRef]
Valentin, F. I. , Anderson, R. , and Kawaji, M. , 2017, “ Experimental Investigation of Convection Heat Transfer in High Pressure and High Temperature Gas Flows,” ASME J. Heat Transfer, 139(9), p. 091704. [CrossRef]
Bruun, H. H. , 1996, Hot-Wire Anemometry: Principles and Signal Analysis, Oxford University Press, Oxford, UK.
McEligot, D. M. , and Bankston, C. A. , 1969, “ Numerical Predictions for Circular Tube Laminarization by Heating,” ASME Paper No. 69-HT-52.
Shehata, A. M. , 1984, “ Mean Turbulence Structure in Strongly Heated Air Flows,” Ph.D. thesis, University of Arizona, Tucson, AZ. https://repository.arizona.edu/handle/10150/187902
Valentín, F. I. , 2016, “Experimental and Numerical Investigations of High Temperature Gas Heat Transfer and Flow in a VHTR Reactor Core,” Ph.D. thesis, Department of Mechanical Engineering, City College of New York, New York. http://adsabs.harvard.edu/abs/2016PhDT........40V
Valentín, F. I. , Artoun, N. , Kawaji, M. , and McEligot, D. M. , 2018, “ Forced and Mixed Convection Heat Transfer at High Pressure and High Temperature in a Graphite Flow Channel,” ASME J. Heat Transfer (epub).
Valentín, F. I. , Artoun, N. , Anderson, R. , Kawaji, M. , and McEligot, D. M. , 2017, “ Study of Convection Heat Transfer in a VHTR Flow Channel: Numerical and Experimental Results,” Nucl. Technol., 196(3), pp. 661–673. [CrossRef]
Lee, J. I. , Hejzlar, P. , Saha, P. , Kazimi, M. S. , and McEligot, D. M. , 2008, “ Deteriorated Turbulent Heat Transfer (DTHT) of Gas Up-Flow in a Circular Tube: Experimental Data,” Int. J. Heat Mass Transfer, 51(21–22), pp. 3259–3266. [CrossRef]
Jørgensen, F. E. , 2002, “ How to Measure Turbulence With Hot-Wire Anemometers: A Basic Guide,” Dantec Dynamics, Skovlunde, Denmark.
Kakac, S. , Shah, R. K. , and Aung, W. , 1987, Handbook of Single-Phase Convective Heat Transfer, Wiley, Hoboken, NJ.

Figures

Grahic Jump Location
Fig. 1

(a) Schematic of open loop experimental setup and (b) placement of a thermocouple and HWA probe for turbulence measurements

Grahic Jump Location
Fig. 2

Hot-wire anemometer probe and thermocouple used for fluid temperature measurement, taken (a) outside and (b) inside the flow channel

Grahic Jump Location
Fig. 3

Test section flow rate in standard liters per minute as a function of time during the data acquisition period for air at 1.7 MPa and 473 K

Grahic Jump Location
Fig. 4

Variations of the ratio of graphite wall temperature to local fluid temperature near the HWA location (plane 9) with the local Reynolds number for (a) air at bulk temperatures of 473 K and (b) N2 at 673 K

Grahic Jump Location
Fig. 5

(a) Wall-to-fluid temperature ratio for nitrogen at 4.76 MPa as a function of Reynolds number for various exit fluid temperatures and (b) Reynolds numbers corresponding to peaks in wall-to-fluid temperature ratio for air and nitrogen at various pressures and constant fluid temperature of 473 K

Grahic Jump Location
Fig. 6

Turbulence intensity of the radial velocity component at two pressures: (a) 2.72 MPa and (b) 1.70 MPa

Grahic Jump Location
Fig. 7

Variations of Reynolds stress and graphite wall temperature in plane 9 with local Reynolds number at 1.70 MPa for local fluid temperatures of (a) 473 K, (b) 423 K, and (c) 373 K

Grahic Jump Location
Fig. 8

Sensors 1 and 2 voltages for air at 2.72 MPa and 125 standard liters per minute. Voltage was translated by subtracting the mean voltage to the acquired voltage.

Grahic Jump Location
Fig. 9

Raw voltage and filtered data after applying a Butterworth filter for (a) sensor 1 and (b) sensor 2

Grahic Jump Location
Fig. 10

FFT of the raw signal representing turbulence for (a) sensor 1 and (b) sensor 2

Grahic Jump Location
Fig. 11

Two examples showing consistent variations of the Reynolds stress and the summation of the frequency spectrum components with Reynolds number for air at (a) 1.70 MPa, 373 K and (b) 2.72 MPa, 423 K

Grahic Jump Location
Fig. 12

Results for air at ambient temperature and 1.70 MPa

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