FLOW BOILING HEAT TRANSFER IN IMPINGING LIQUID JET FLOWS Udo Fritschinga, Paul Starkb a
Particles and Process Engineering, Univ. Bremen, Institute of Materials Science, Badgasteiner Str. 3, 28357 Bremen, Germany. Email:
[email protected] b Institute of Materials Science, Badgasteiner Str. 3, 28357 Bremen
ABSTRACT Heat transfer process during quenching of solid bodies in evaporating liquid may be considerably influenced by boiling phenomena. Starting from high surface temperatures above the Leidenfrost temperature different boiling phases arise during the cooling process (film, transition, and nucleate boiling, and convection). The aim of the investigation is to analyse how these heat transfer phases are distributed in space and time for the quenching of a surface by an impinging jet flow. Therefore, the liquid/vapour twophase flow and heat transfer process during flow boiling is modelled and the process is simulated. A mixture model is utilized to determine the evaporation process and the local volume fractions of vapour and liquid in the flow. Based on this model the heat transfer rate in all stages of boiling and convection may be calculated for various flow conditions. The impinging submerged jet flow and the conjugate heat transfer from a flat substrate plate and the resulting temperature distribution inside the plate are simulated with respect to the transient boiling phase distribution. The influence of the liquid subcooling temperature, the plate thickness, and the conductivity of the solid substrate material on the transition region positions (e.g. the Leidenfrost point) and the transition temperatures are analysed, respectively.
1. INTRODUCTION The impinging jet cooling process is utilized in e.g. quenching of specimen and structures that have been heated to temperatures certainly above the Leidenfrost point. During quenching from a temperature substantially above the liquid Leidenfrost temperature different boiling phases arise. In the initial phase a continuous vapour layer or vapour film on the specimen surface is formed. The vapour layer formation in particular sections of the flow is causing low heat transfer rates (film boiling). When the wall temperature decreases below the Leidenfrost temperature the vapour film collapses and the surface rewets. This cooling/boiling (transition and nucleate boiling) stage is characterized by the direct contact between wall and fluid while a considerable amount of bubbles is generated and immediately carried away from the surface. In the last phase, at temperatures below the boiling temperature, pure convective heat transfer from the specimen occurs. During the quenching process, the different boiling stages may not occur subsequently, but may occur simultaneous at different parts. This distribution leads to very high variations of heat transfer rates and causes complex gradients in heat transfer at the surface and temperature distributions in the solid.
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The main aim of the investigation is to investigate how these heat transfer phases are distributed in space and time. Therefore, the liquid/vapour two-phase flow and heat transfer process during flow boiling is modelled and the process is simulated. Special emphasis in the simulations is on the role of impinging jets to control the boiling stages and heat transfer processes. A mixture model is utilized to determine the evaporation process and the local volume fractions of vapour and liquid in the flow. Appropriate sink and source terms describing the phase transformation for evaporation and condensation (water/vapour) were included in the mass and momentum conservation equations. In submerged jet flows (the liquid and the surrounding medium are identical) the surrounding liquid is partially accelerated and entrained by the jet flow. The core flow conditions in front of the nozzle only remain almost constant within a distance of 4-6 nozzle diameters (“core length”). Further downstream, the jet spreads, the velocity profile widens and the maximum velocity on the jet centerline decreases due to friction and viscous effects. For the resulting flow structure and the associated heat transfer process regimes during jet impingement onto a hot flat substrate plate (Twall > Tsat) three boiling zones can be identified [1-3] (see fig. 1): • Wetted zone: Around the stagnation zone of the jet flow a circular region with sufficiently low surface temperature is present, so that no liquid evaporation is occurring. • Boiling width: For higher distance to the stagnation point, a ring-shaped region can be identified in which highly unsteady nucleation boiling occurs. • Unaffected zone: For sufficiently high distances to the stagnation region, the plate surface is not yet influenced by the incoming jet flow. The wall is covered by vapor film and the surface temperature is still close to the initial wall temperature. Within this work the boiling phase distribution for the submerged jet case are investigated (liquid jet in liquid reservoir). The nozzle parameters (diameter, outlet velocity, nozzle distance) are kept constant, so that the influence of the liquid subcooling and the solid material properties are investigated. The role of impinging jet flow on the control of heat transfer and boiling stages is illustrated.
Fig. 1: Boiling zones within jet impingement on a heated substrate
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2. NUMERICAL MODEL An integral multiphase modeling approach is utilized to develop one comprehensive heat transfer model for all occurring boiling phases [4, 5]. Thus, an Eulerian multiphase flow model is used. In contrast to conventional Volume-of-Fluid models (VOF), no distinct phase boundary between the liquid and the vapor phases is calculated explicitly, but the local volumetric phase fractions are determined for each position in the domain as (eq. 1): α liq =
Vliq Vliq + Vvap
; α vap =
Vvap Vliq + Vvap
, where
α +α = 1 . liq
vap
(1)
In this approach, the vapor phase is always treated as an accumulation of vapor bubbles. At high vapor fractions the intense crowding of bubbles forms a continuous vapor region with vapor volume fractions close to unity (αvap → 1). It is assumed that the heat transfer mechanism in this region is related to the film boiling regime (radiation heat transfer is neglected). In the nucleate or transition boiling regime for 0 < αvap < 1, the dispersed behavior of the vapor-liquid two-phase flow is intrinsically reflected. If αvap → 0, single-phase liquid flow mechanisms are utilized for the calculation of the flow field and the pure convective heat transfer from the wall. The Eulerian multiphase model approach considers continuity, momentum and energy conservation for each phase (here: liquid and vapor). The phases are treated incompressible with temperature dependent properties. While both phases can develop an individual velocity and temperature field, a common pressure field is shared. The coupling of the phases is achieved through interphase exchange terms for momentum and heat that appear in the conservation equations. The exchange and coupling coefficients are determined by assuming that the vapor phase is a dispersed phase with spherical bubbles of diameter db. Correlations from literature are used to calculate the momentum exchange (Schiller-Naumann-correlation) and heat transfer (Ranz-Marshall-correlation) between the phases [6-8], both depend on the bubble Reynolds number Reb: Re b =
r r ρ liq u liq − u vap d b η liq
.
(2)
Here, the relative velocity between the phases as well as the density ρliq and the dynamic viscosity ηliq of the liquid phase are required. Source terms in the conservation equations are necessary to include the mass transfer between the liquid and vapor phase due to evaporation and condensation. Within the developed model it is assumed that the local liquid temperature Tliq within any cell of the numerical grid must not exceed the saturation temperature Tsat. To maintain this temperature limit within any time step Δts, the following sink term is applied in the energy conservation equation: if Tliq > Tsat : q& lim it , liq = −α liq ρ liq c p, liq
Tliq − Tsat Δt s
.
(3)
A critical heat flux is defined (see eq. 4) to decide within any given time step whether the supplied local heat flux is sufficiently high to enable additional vapor formation or if condensation is dominant.
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q& crit = −α liq ρ liq c p, liq
(ΔT ) Δt s
.
(4)
Within the developed boiling model it is checked for each cell in the computational domain within each time step of the calculation, if the absolute value of the heat flux to limit the liquid temperature as defined in eq. 3 is higher than the critical heat flux from eq. 4. If this is fulfilled, evaporation is dominant. Otherwise, condensation is dominant independently from the vapor temperature in that cell. Additionally, when the averaged vapor temperature Tvap in a cell drops below saturation temperature Tsat (at ambient pressure level pliq) immediate and complete recondensation of the remaining vapor takes place. The amount of transferred mass is calculated based on the latent heat of the fluid Δhv. The sinks and source terms in the energy and mass equation are summarized in table 1. Table 1: Sinks for evaporation / condensation in mass and energy conservation of the liquid Condition
Sink term in energy equation
Sink term in mass equation
Evaporation
if q& lim it ,liq < q& crit
Se = q& lim it ,liq
Sm = ε
condensation I
if q& lim it ,liq > q& crit
Se = q& lim it ,liq − q& crit
Sm =
condensation II
if Tvap < Tsat
Se =
− α vapρ vap Δh v Δt s
Sm =
Se Δh v
q& lim it ,liq − q& crit Δh v Se Δh v
The source term for vapor formation Sm contains a numerical under relaxation factor ε that has been found to be essential for numerical stability in order to allow appropriate expansion of the formed vapor phase. The under relaxation parameter has been adjusted to ε = 0.1.
2.1 Model implementation, geometry and boundary conditions The model implementation is performed within Ansys Fluent 13, Service Pack 2. Sinks and sources in the conservation equations have been incorporated by user-defined functions (UDF). An Eulerian-Eulerian multiphase flow model is applied with (liquid) water as the primary and water vapor as the secondary phase. Simulations are performed for an impinging jet arranged perpendicular to a flat substrate plate located in a closed system filled with water at atmospheric pressure conditions. This condition is named a submerged jet, the whole domain always is filled with water, the jet is submerged in a water reservoir. The simulations are performed in a two-dimensional, axisymmetric approach (see fig. 3). The parameters and values under investigation are shown in in fig. 3 and summarized in table 2.
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Fig.: 3: Geometry and boundary conditions for submerged impinging jet The numerical mesh in the near-wall region for y ≤ 1 mm is of a rectangular nature. The flow solution has been proved to be mesh-independent at this spatial grid resolution. Table 2: Geometric parameters d
H
B
Br
Hy
h
5 mm
4d
24 d
40 d
40d
0.5…15 d
The nozzle distance to the flat plate H and the outlet velocity v0 (without profile) are varied to investigate their influence on the time-dependent vapor formation and heat transfer rates. The specific values of the varied parameters are summarized in table 3. The nozzle Reynolds number Red is defined as: Re d =
ρ liq v 0 d η liq
.
(4)
Red is calculated with the liquid phase properties (water) at inlet conditions and the nozzle diameter d. The turbulent structure of the flow is modeled by the standard k-ε-model with enhanced wall treatment (dimensionless wall distance of the first cell row on the hot wall y+ ≤ 5) [12]. Table 3: Parameters during numerical simulation Inflow turb. level
vnozzle
Red
[m/s]
[-]
Tu [%] 5
2
Tsub =
wall superheat (at t = 0 s)
Tsat - Tliq,0
Prd
[K]
[-]
40
3.03
21600
h/d
λsolid
[-]
[W/(m K)]
[K] 18…36 (steel) 0.5…15
80
7.02
Tsup = Twall - Tsat
800 K 380 (copper)
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The multiphase pressure-velocity coupling scheme is applied to solve the conservation equations, whereas a second-order scheme is used for the convective terms. Appropriate temperature-dependent material properties for the liquid and vapor phase of water, and for a non-transforming austenitic steel (1.4305) and copper material of the substrate plate are utilized as given in [11, 13]. The Prandtl-number of the liquid at inlet conditions is Pr (Tsub = 40 K) = 3.03, respectively Pr (Tsub = 80 K) = 7.02. At the beginning of the calculation (t = 0 s), the entire domain is initialized at αliq = 1, Tsub = 40 K and v = 0 m/s. The hot plate is set to exhibit a homogenous superheat temperature Tsup = 800 K. Within the unsteady cooling simulation the conjugate heat transfer problem with interaction between the temperature distribution inside of the plate and the flow above is solved. Therefore, a constant time step size of Δt = 5·10-5 s is used.
3. RESULTS 3.1 Identification of different boiling zones on the hot wall
For illustration of the different boiling zones Fig. 4 shows the vapor fraction distribution on the surface (first grid cell) at time t = 2 s and t = 4 s for a moderate nozzle outlet velocity and nozzle to plate distance. Around the impinging jet stagnation zone at r / d = 0, a fully-wetted area (1) can be identified where the vapor fraction is αvap = 0. The impinging liquid jet almost immediately causes the vapor film to collapse and the surface becomes wetted by the liquid. For higher distances to the center region, a transition zone (2) with highly fluctuating vapor fractions (both over time and area) indicating highly unsteady (nucleate) boiling phenomena can be identified. Due to the circular setup, this boiling region is ring shaped with its outer edge characterized by the transition to the film boiling region (3) with vapor fractions close to unity (αvap → 1). The transition region between the boiling width zone and the vapor film region can be associated with the Leidenfrost effect. These regimes and boiling zones can be similarly identified for all simulated cases of liquid jet impingement cooling.
Fig. 4: Vapor fraction distribution immediately on the plate surface during unsteady simulation at t = 2 s (a) and t = 4 s (b); three different zones on the plate surface (c) From the simulation results, the transition points between the different boiling zones were derived. The radial position with the first steep increase from vapor fractions αvap = 0 to higher values of αvap is associated with the transition from the wetted region (1) to the boiling width zone (2). Similarly, a critical vapor fraction level of αvap = 0.95 has been assigned to detect the transition point from the boiling width zone (2) to the vapor film zone (3).
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3.2 Influence of liquid subcooling on time-dependent movement of the boiling zones
The positions of the transition region between the boiling zones (see fig. 4) on the hot plate during submerged jet cooling in water are summarized in fig. 5 (left). Here, t = 0 s is defined as the time when the nozzle flow starts. The solid lines represent the transition from the wetted zone (1) to the boiling width zone (2). The dashed lines indicate the transition region between the boiling width region (2) and the film boiling zone (3). The boiling process with highly unsteady vapor formation is occurring within the boiling width zone (2), this zone is associated with nucleation or transition. For Tsub = 40 K and Tsub = 80 K, the formation of a fully wetted zone and the surrounding boiling width zone is starting immediately after the developing jet flow is impinging onto the hot flat substrate. In the stagnation region at r / d = 0, the jet flow momentum is sufficiently high to cause the formed vapor layer to immediately collapse. The wall-near liquid layer in the wetted zone is heated with increasing distance to the center of the plate r / d. For increasing time and distance to the stagnation zone, the growth rate of the wetted zone is gradually decreasing while the diameter of the boiling width stays more or less constant. Around the jet stagnation region (at small values of r / d) the jet flow is able to cause the break-down of the vapor film. The incoming jet velocities result in lower residence times of the liquid phase in the initially highly superheated wall regions. This is preventing the liquid phase from being heated extensively, thus suppressing additional vapor generation, lower heat transfer rates and – in summary – a less quick growth of the wetted zone and the boiling width. In consequence, the doubling of the liquid subcooling Tsub leads to a faster spreading of the boiling regions and to a larger boiling width for any given position on the substrate plate.
Fig. 5: Time-dependent position of transition regions (left) and local temperatures (right) at transition transitions regions (Red = 21600, h / d = 15, material: steel, λsolid = 27 W / (m K)) The corresponding surface temperature in the transition region between the fully wetted zone (1) and the boiling width (2) and the temperature in the transition region from nucleate boiling (2) to film boiling (3) (Leidenfrost temperature) were determined from the numerical simulations and the results are illustrated in fig. 5 (right). All cases illustrate a decreasing transition temperature for increasing distances from the stagnation zone. For a given position
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on the plate the transition temperature in both transition regions is generally higher for Tsub = 80 K compared to Tsub = 40 K. 3.3. Influence of plate material (solid conductivity) and plate thickness
In a parameter variation, the plate thickness h / d and the conductivity λsolid of the solid are varied, while the jet nozzle parameters are kept unchanged. The resulting rewetting front movement is shown in fig. 6. At λsolid = 27 W / (m K) (fig. 6, top row), representing a typical value for a steel substrate, an increasing thickness of the plate from h / d = 0.5 up to h / d = 2 results in decreasing growth rates of the wet zone (1). In opposite, a further increase of the substrate plate thickness to h / d = 15 does not lead to any significant changes in the wetting behavior, the qualitative behavior and shape of the curves is generally very similar. The relatively low solid conductivity in this case limits the ability of transporting the thermal energy from the core to the wall region as well as in the direction parallel to the surface. Within the simulated time frame t ≤ 4 s, heat is still being transported from the core region to the wall region as well as from near-wall regions still covered with a closed vapor film to the center regions of the plate, so that for sufficiently high wall thicknesses the core region is still at the initial solid temperature and thus it is limiting the rewetting process. Accordingly, the very high cooling intensity in the wetted zone and in the boiling width cause high temperature gradients both in wall-normal and wall-parallel direction.
Fig. 6: Time-dependent positions of transition regions s (Red = 21600, h / d = 15, Tsub = 40 K)
At λsolid = 380 W / (m K) (related to copper) and h / d ≤ 1, the same qualitative shape of the curves is observed as shown for steel. The high conductivity is efficiently providing the heat
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from the core region to the plate surface. The entire cross section of the plate has to be cooled down to the transition temperature by the jet flow before the vapor film collapses. As a result, temperature gradients are then mostly present in wall-parallel direction. In contrast, at h / d = 2 a time delay of Δt ≈ 2 s can be observed until the growth of the boiling width begins, whereas for h / d = 15 no growth of the boiling regions can be observed within the simulated time frame. 3.4 Surface Temperature profiles
The resulting temperature profiles on the plate surface for two time steps are illustrated in fig. 7. As described above, the vapor layer is formed before the jet flow approaches the plate surface. As soon as the jet flow is impinging on the substrate it pushes away the vapor layer in the stagnation zone. The direct contact between the liquid and the plate in the wetted region (1) and the boiling width is enabling very high cooling intensities. For steel as the substrate material (fig. 6, top) the low cooling intensities result in high temperature gradients, whereas the higher conductivity of copper (fig. 6, bottom) enables the efficient transportation of the heat from the outer regions of the plate surface as well as from the core region to those parts of the plate surface where the vapor film has already collapsed before.
Fig. 7: Surface temperature profiles (Red = 21600, h / d = 1, Tsub = 40 K) 3.5 Surface temperature in transition regions
The surface temperature in the transition region between the wetted zone (1) and the boiling width zone (2) as well as the temperature in the transition region from the boiling width (2) to film boiling (3) (Leidenfrost temperature) have been analyzed from the numerical simulations (see fig. 4) and are illustrated in fig. 8. For the thermal properties of the substrate materials under investigation, the curves show a decreasing transition temperature for increasing distances from the stagnation zone. For a given substrate material, the plate thickness does not lead to any significant changes in the transition temperature in both transition regions. Furthermore, when comparing the curve
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shape for both solid materials no significant influence on the transition temperatures can be stated. Even though the wetting kinetics (fig. 5) and the temperature field (fig. 6) on the plate surface are fundamentally different, the transition temperatures do not reflect this behavior. 3.6 Surface temperature gradients in transition regions
The local temperature gradient in wall-parallel direction on the plate surface at the position of the rewetting fronts has been evaluated from the numerical simulation. The results are illustrated in fig. 9. Around the stagnation zone of the impinging jet, an almost instantaneous formation of both the wetted zone (1) and the boiling width (1) is observed (compare fig. 7) after the jet impinges on the substrate. Afterwards, the intense cooling intensity of the jet flow results steeply in increasing temperature at the outer edges of these zone. Relatively low solid conductivities of steel lead to maximum temperature gradients up to 220 K / mm at the transition from zone (1) to (2) at r / d ≈ 1 respectively 310 K / mm at the transition from zone (2) to (3) at r / d ≈ 2.5. For higher distances of the transition regions to the stagnation zone, the lower cooling intensities of the liquid jet flow leads to decreasing temperature gradients. In accordance to the trends described above, these values are significantly lower for copper substrate, but generally show the same behavior.
Fig. 9: Local temperature at transition regions (Red = 21600, h / d = 15, Tsub = 40 K)
Fig. 10: Surface temperature gradients (in wall-parallel direction) at transition regions (Red = 21600, h / d = 1, Tsub = 40 K)
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4 CONCLUSIONS
The liquid jet impingement and heat transfer processes with boiling phenomena on a superheated flat substrate plate (Twall > Tsat) were investigated. The submerged jet case is studied where a liquid jet enters a liquid reservoir. A multiphase flow and heat transfer model is described in which the conservation equations were modified with sink and source terms to include evaporation and condensation effects. The vapor phase is modeled in terms of a bubble crowd approach to properly analyze all occurring boiling regimes and phases during the jet cooling process within one single model approach. The influence of the liquid subcooling (40 K ≤ Tsub ≤ 80 K), the plate thickness (0.5 ≤ h / d ≤ 15), and the conductivity of the solid substrate material (18 W / (m K) ≤ λsolid ≤ 380 W / (m K)) on the transition region positions (e.g. the Leidenfrost point) and the transition temperatures are analysed, respectively. Depending on the plate thickness and solid material, the time-dependent boiling phase distribution on the surface as well as the resulting temperature field inside of the substrates were investigated for submerged jet flow conditions. Even though the temperature distribution heavily varies with respect to the solid conductivity of the plate material, no significant influences on the transition temperatures between the boiling phases (including the Leidenfrost temperature) can be observed.
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