Abstract

Impinging jet nozzles are omnipresent in industrial applications. Innovative impinging jet nozzles, such as radial jet reattachment (RJR) and slot jet reattachment (SJR) nozzles, have been proven to be highly efficient tools to enhance heat and mass transfer, compared to traditional in-line jet and slot-jet nozzles. However, the heat and mass transfer in the region immediately underneath these reattachment nozzles are relatively inefficient. The ionic wind is a promising technique for heat transfer enhancement. The ionic flow is induced when free ions are accelerated by an electric field, and exchange momentum with neutral air molecules. In this numerical study, the performance of the SJR nozzle is improved by the application of an electric field, specifically, ionic wind, which is generated in the region directly between the nozzle and the exposed impingement surface. The two-dimensional numerical model is based on the flow field generated by an ionic wind-assisted SJR nozzle. The simulation results show a significant secondary flow induced under the nozzle, due to ionic wind. A significant enhancement of local and average heat transfer coefficients is achieved. The heat transfer increases with the applied potential and nozzle exit velocity. However, the SJR flow pattern is altered when the air exit velocity is below a certain threshold. The simulation results provide an in-depth understanding of the heat transfer characteristics under various operating conditions and pave the way for developing this novel impinging nozzle design.

Introduction

Impinging jets are used extensively in various industrial activities, and their characteristics have been investigated for several decades. Their applications include cooling of electronic components, turbine blades, as well as the drying of forestry, food, agricultural, pharmaceuticals, and chemical products. Traditional impinging jet nozzles generally contain geometries that are axisymmetric (pipe or circular orifice shape) or slot jets (two-dimensional). There has been much numerical and experimental work about heat transfer characteristics with conventional in-line jet and slot jet (SJ) nozzles. Martin et al. summarized the heat and mass transfer characteristics of single nozzle and arrays of nozzles and listed empirical correlations for mean and local heat transfer coefficients [1]. Baughn et al. extended the experimental scope and investigated the effects of crossflow, jet orientation, jet temperature, as well as various surface shapes [2]. Colucci et al. studied the effects of nozzle geometry, Reynolds number, and nozzle-to-plate spacing on the local heat transfer coefficients for confined air jets [3]. Later, Brignoni and Garimella extended the study of nozzle geometry and found that the chamfered nozzles achieved 20%∼30% heat transfer enhancement with the Reynolds number varies from 5000∼20,000 when compared to nonchamfered nozzles [4]. Another relevant research showed the elliptic cross-sectional area nozzle showed ∼15% heat transfer enhancement than that of circular nozzle [5]. Ekkad and Singh described multiple approaches, including nozzle shape, contouring, orientation, roughness, etc., for nozzle effectiveness improvement in their recent work [6]. However, one of the major drawbacks of using these jet impinging nozzles lies in the high pressure exerted on the impingement surface. For certain applications such as drying fragile products, it is essential to avoid a high exertion of pressure. Thus, the maximum mass flow rate must be confined below a certain threshold, which leads to reduced heat and mass transfer performance. There have been many other attempts at altering the impinging jet flow field to protect the sample as well as to enhance the transport characteristic of conventional nozzles. Examples of these innovative nozzles are radial jet reattachment (RJR) and slot jet reattachment (SJR) nozzles. The concept of reattachment nozzles dates back to the early 1980s, mainly with the work of Page et al. [7]. The work was further continued to determine the heat and mass transfer characteristics of RJR and SJR nozzles under various operating conditions. The SJR nozzle is the two-dimensional version of the RJR nozzle, and the heat transport characteristics of these nozzles have been well understood [79].

A typical SJR nozzle design is shown in Fig. 1. In the SJR nozzle, the air jet is directed outward from the exit of the nozzle and reattaches onto an adjacent surface in its vicinity. The turbulent mixing at the boundaries of the air stream induces flow by mass entrainment, which induces a cross-sectional oval-shaped reattachment region at a close nozzle-to-surface spacing. Part of the airstream at this region recirculates under the nozzle, while the rest flows in an outward direction [10]. Due to the induced stream, the pressure in the recirculation region is lower than the ambient atmospheric pressure, as shown in Fig. 2. The predominant characteristic of reattachment nozzles is that a net-zero or even negative force can be exerted on the reattachment surface by varying the exit angle of the nozzle. It is noted that a fair comparison should include the additional pressure drop in the SJR nozzle due to the deflection of fluid flow by the bottom plate, thus, the comparison based on the identical fluid flow power or peak pressure is made. The SJR nozzles exert significantly less pressure on the surface, as compared to the SJ nozzle, under identical flow power. The air flow power for the SJR nozzle needs to increase from 45 W to 190 W to exert identical exerted air pressure on the impingement surface as the case with the SJ nozzle. Under the matched peak pressure, the SJR nozzle provided much better heat transfer in comparison to the SJ nozzle, as shown in Fig. 3. It is important to note that both SJ and SJR nozzles were compared at their optimal heights from the impingement surface. However, in the recirculation region, both local and average heat transfer coefficients of the SJR nozzle were less effective.

Fig. 1
Schematic of slot-jet reattachment nozzle
Fig. 1
Schematic of slot-jet reattachment nozzle
Close modal
Fig. 2
Comparison of surface pressure distribution of slot-jet and SJR nozzles with 0 deg exit angle
Fig. 2
Comparison of surface pressure distribution of slot-jet and SJR nozzles with 0 deg exit angle
Close modal
Fig. 3
Comparison of local and area-averaged heat transfer coefficients of slot-jet and SJR nozzles with 0 deg exit angle under identical surface peak pressure of 800 Pa
Fig. 3
Comparison of local and area-averaged heat transfer coefficients of slot-jet and SJR nozzles with 0 deg exit angle under identical surface peak pressure of 800 Pa
Close modal

The electrohydrodynamic (EHD) phenomenon involves the interaction between the fluid flow and the electric field. Most of the existing EHD research makes use of ionic wind. When a high voltage is applied to a sharp emitting electrode (wire- or needle-shaped), the air near the electrode becomes ionized, and the excited free ions are driven to the collecting electrode by Coulomb force. Collisions between the ions and the neutral air molecules cause a momentum transfer, thus creating a plume-like gas flow, called corona/ionic wind [11]. The formation of ionic wind and the resultant flow field has been widely investigated, both experimentally and numerically [1217]. Lai and Lai adopted wire electrodes for drying and concluded that the air stream flowing over the sample surface reduced the impact of the electric field because the corona wind flow is suppressed and confined to a rather narrow region along the wall [18]. Shi et al. numerically studied the ionic flow field with a multiple-pin-plate configuration and presented the relationship between the air mass flux and the applied voltage [19]. Go et al. experimentally and analytically studied the performance of ionic wind in the presence of a parallel external flow. Their results showed that ionic wind can increase the local heat transfer coefficient in a laminar external flow by a factor of 2 and illustrated the dependence of heat transfer enhancement on the electrode spacing [20]. Additionally, parametric studies were carried out to understand the impact of emitter radius, electrode distance, length, and applied polarity for a wire to cylinder configuration corona discharge [21]. Recently, A multineedle-ring type of electrode configuration was investigated and the results showed that in the electronic components heat dissipation application, the ionic wind velocity is dependent on the electrode materials, needle numbers, and electrode spacing [22]. Besides this work, a wire-to-double-cylinder configuration ionic wind pump showed 2.6 times heat transfer coefficients enhancement, a higher energy efficiency of 2.6% was also reported [23]. Although EHD flow is a promising novel approach for heat transfer enhancement, the applied electric potential should be controlled to prevent the occurrence of an electrical avalanche, which limits the magnitude of the ionic wind velocity to several meters per second. Because of this upper-velocity limitation, replacing existing turbulent convective impingement techniques with ionic wind electrodes will not create substantial benefits on the heat transfer characteristic. However, regarding the low heat and mass transfer in the recirculation region under the bottom plate of the SJR nozzles, the installation of ionic wind electrodes could locally induce a secondary flow, which could augment the circulation and enhance the overall heat transfer characteristic.

The main objective of this study is to further enhance the heat transfer characteristics of SJR nozzles by the application of an electric field. Specifically, the ionic wind is generated within the recirculating zone of an SJR nozzle, and its influence on the heat transfer of the impingement surface is numerically investigated. The ionic wind-assisted SJR nozzle momentum and energy equations are coupled with the electrostatic equations to provide an in-depth understanding of the fluid flow pattern and heat transfer characteristics under various operating conditions. The impact of the ionic wind on the flow entrainment beneath the SJR nozzle and the flow reattachment on the impingement surface is also investigated.

Theoretical Model

To make the highest impact of ionic wind on the SJR nozzle performance, the electrodes are considered to be in the recirculation zone where the corresponding heat transfer is minimal. The symmetric schematic of an ionic wind-assisted SJR nozzle is presented in Fig. 4. A hot air stream exits the nozzle with an angle of 20 deg and then reattaches on the reattachment plate below. The jet exit width (be) is assumed to be 4 mm. The optimal nozzle-to-surface spacing (Xp) of the SJR nozzle is based on the experimental data reported by Narayanan et al. [8]. Twelve cylindrical wire-shaped electrodes, with a diameter of 0.5 mm, are installed 4 mm above the impingement surface, inside the recirculation region. The installation height is selected to avoid electrical breakdown. The spacing between neighboring electrodes is 1 mm and the impingement surface is assumed to be electrically grounded. The theoretical model assumes the flow to be continuous, incompressible, and laminar.

Fig. 4
Schematic of ionic wind-assisted SJR nozzle
Fig. 4
Schematic of ionic wind-assisted SJR nozzle
Close modal

Governing Momentum and Energy Equations.

The ionic wind generation involves the interaction of the electric field and the flow field. This interaction between electric field induces the fluid flow motion by electric body force (i.e., Coulomb force), given below in the following equation:
fe=ρeE
(1)

where ρe and E represent the electric charge density and the electric field vector, respectively.

The electrostatic field can be calculated from the classical Poisson's equation
2φ=ρeεe
(2)
In Eq. (2), ions discharged from the wire electrode surface provide the mechanism for generating ionic wind. Thus, it is necessary to determine the space charge density. Since the charge density distribution in the vicinity of the emitting electrodes is complicated, the most common approach is to formulate the required boundary conditions for ions at the surface of the electrodes [14]. The charge density at the surface of the wire electrodes can be derived either from an experimentally measured electric current value or from a semi-empirical approximation. The latter approach is adopted in this study. The charge density is determined using Kaptzov's hypothesis, which states that once the electric potential applied to the emitter electrodes exceeds the onset electric potential, the corona starts to discharge while the electric field at the wire surface remains constant [24]. This critical electric field strength can be predicted by the semi-empirical Peek's formula [25]. The critical electric field, Ew, for a cylindrical wire is given by the following equation [2629]:
Ew=E0(1+0.308rw)
(3)
where E0 equals to 3.1 × 106 V/m, and rw represents the radius of the wire electrode. The electric field E is linked to the negative gradient of the electric potential, as shown in the following equation:
E=ϕ
(4)

In this study, Eqs. (2) and (4) are iteratively solved to get accurate charge density, ρe, until the electric field strength at the surface of the wire electrodes is close to the critical electric field strength value, Ew, predicted by Peek's formula.

Once the charge density is specified at the electrode surface, the transport of ions or conservation of charges is described by the following equation:
·(ρebE+ρeuDρe)=0
(5)

where the three terms on the left-hand side of the equation represent charge conduction (movement of ions in the electric field), charge convection (ion transport due to the air flow), and charge diffusion (ion migration, due to the electric charge concentration gradient), respectively. In this study, the charge convection term is neglected, due to the minimal characteristic velocity [11].

The Navier–Stokes equations are coupled with the classical electrostatic equations through the Coulomb force, ρeE, acting as a body force. The continuum and momentum equations are given as follows:
·(ρu)=0
(6)
·(ρuu)=·μuP+ρg+ρeE
(7)
The induced Joule heating is included as a source term in the energy equation, given below:
u·(ρcp,airT)=k2T+bρeE2
(8)

where cp,air, k, and b represent the specific heat of air, the thermal conductivity of air, and ion mobility, respectively.

To investigate the influence of ionic wind generation on the convective heat transfer underneath the SJR nozzle bottom plate, the heat transfer coefficient on the impingement surface is determined. The temperature differential is related to the corresponding local convective heat transfer coefficient, which is defined as the following equation:
hloc=q0`TsT0
(9)

where q0 is the local heat flux on the impingement surface, and Ts and T0 represent the local impingement surface temperature and the air temperature at the SJR nozzle exit, respectively.

The average heat transfer coefficient is calculated based on the area average of the local heat transfer coefficient along the x axis, as shown in the following equation:
havg=1x0xhlocdx
(10)

Boundary Conditions.

To reduce the computational cost, half of the ionic wind-assisted SJR nozzle domain was considered in this study, as depicted in Fig. 5. The dimensions of the computational domain are taken sufficiently large to eliminate the influence of domain size on the electric potential, space charge as well as fluid flow distribution. The boundary conditions are required for the electric field, the space charge field, and the airflow field, and the temperature field. These boundary conditions (BCs) and their corresponding mathematical formulations (MFs) are listed in Table 1.

Fig. 5
Numerical domain of ionic wind-assisted SJR nozzle simulation
Fig. 5
Numerical domain of ionic wind-assisted SJR nozzle simulation
Close modal
Table 1

Boundary conditions and mathematical formulations in an ionic wind-assisted SJR nozzle simulation

Electric fieldSpace chargeAir flowTemperature
Boundary regionsBCsMFsBCsMFsBCsMFsBCsMFs
Wire electrodesSpecified electric potentialΦ=ΦwireSpecified charge densityρe=ρe,wireNo slipu=0Thermally insulatedn·T=0
Impingement surfaceGround electric potentialΦ=0No fluxn·ρe=0No slipu=0Specified heat fluxq″=q0
Air inletZero chargen·Φ=0No fluxn·ρe=0Velocityu=u0Specified temperatureT=T0
Air outletZero chargen·Φ=0No fluxn·ρe=0Pressurep=p0Thermally insulatedn·T=0
SJR nozzle bodyGround electric potentialΦ=0No fluxn·ρe=0No slipu=0Thermally insulatedn·T=0
SJR bottom plateGround electric potentialΦ=0No fluxn·ρe=0No slipu=0Thermally insulatedn·T=0
SJR nozzle centerlineSymmetricn·Φ=0No fluxn·ρe=0Symmetricn·u=0Symmetricn·T=0
Electric fieldSpace chargeAir flowTemperature
Boundary regionsBCsMFsBCsMFsBCsMFsBCsMFs
Wire electrodesSpecified electric potentialΦ=ΦwireSpecified charge densityρe=ρe,wireNo slipu=0Thermally insulatedn·T=0
Impingement surfaceGround electric potentialΦ=0No fluxn·ρe=0No slipu=0Specified heat fluxq″=q0
Air inletZero chargen·Φ=0No fluxn·ρe=0Velocityu=u0Specified temperatureT=T0
Air outletZero chargen·Φ=0No fluxn·ρe=0Pressurep=p0Thermally insulatedn·T=0
SJR nozzle bodyGround electric potentialΦ=0No fluxn·ρe=0No slipu=0Thermally insulatedn·T=0
SJR bottom plateGround electric potentialΦ=0No fluxn·ρe=0No slipu=0Thermally insulatedn·T=0
SJR nozzle centerlineSymmetricn·Φ=0No fluxn·ρe=0Symmetricn·u=0Symmetricn·T=0

Numerical Simulations of Ionic Wind Assisted Slot Jet Reattachment Nozzle.

The modeling work in this study employs a finite element-based commercial software, comsolmultiphysics, version 5.5. Since this model deals with multiphysics phenomena, namely, electric field, ion transport, air flow, and heat transfer, these physics are solved sequentially to allow for numerical convergence and stability. Similar efforts in terms of analyzing impinging jet flows or ionic wind were carried out by various literature [22,3032]. A total of 86,613 elements were built for the computational domain. At first, the electric potential and ion transport were solved together as a stationary problem. A parametric study of the surface charge density at the electrode surface was performed to match with the critical electric field strength predicted by Peek's formula. Then, the resultant air flow from the nozzle and the ionic wind flow under the nozzle bottom plate, as well as the heat transfer, were solved as a stationary problem. The key parameters in the simulation are listed in Table 2.

Table 2

Key parameters in the ionic wind-assisted SJR nozzle simulation

The exit angle of SJR nozzle, θ20 deg
Exit opening of the nozzle, be4 mm
Average air velocity at nozzle exit,u03 m/s
Spacing between the bottom plate and impinging surface9 mm
Diameter of wire electrodes, rw0.5 mm
Spacing between neighboring electrodes0.5 mm
Spacing between electrodes to the impinging surface4 mm
Applied potential,Φwire8 kV
Impinging air temperature, T0283 K
Ambient temperature, Tamb293 K
Heat flux at impinging surface, q0100 W/m2
Charge density at wire electrode surface, ρe,wire1.34 × 10−3 C/m3
Ion mobility, b1.8 × 10−4 m2/V·s [28]
Ion diffusivity, D5.3 × 10−5 m2/s [28]
The exit angle of SJR nozzle, θ20 deg
Exit opening of the nozzle, be4 mm
Average air velocity at nozzle exit,u03 m/s
Spacing between the bottom plate and impinging surface9 mm
Diameter of wire electrodes, rw0.5 mm
Spacing between neighboring electrodes0.5 mm
Spacing between electrodes to the impinging surface4 mm
Applied potential,Φwire8 kV
Impinging air temperature, T0283 K
Ambient temperature, Tamb293 K
Heat flux at impinging surface, q0100 W/m2
Charge density at wire electrode surface, ρe,wire1.34 × 10−3 C/m3
Ion mobility, b1.8 × 10−4 m2/V·s [28]
Ion diffusivity, D5.3 × 10−5 m2/s [28]

The electric potential and space charge density distribution were solved with a fully coupled direct solver, relying on the multifrontal massively parallel sparse direct solver. The laminar fluid flow field was solved using the parallel direct sparse solver interface. The relative tolerances for flow fluid, flow temperature, and the electric field studies were 10−4.

The sensitivity analysis and mesh-independent tests were performed in such a way that the final solution does not change with the change of tolerance and mesh quality. The mesh-independent study was conducted by solving governing equations on three numerical meshes, with 63,736, 86,612, and 158,831 triangular elements. The test results showed less than 1% variation in the pressure distribution of the impingement surface under a regular SJR nozzle. Thus, the results presented in the following section have been obtained with the grid size based on 86,612 elements.

Results and Discussions

Figure 6 shows the simulation results of the electric field distribution of the ionic wind-assisted SJR nozzle. In Fig. 6(a), the electric potential magnitude gradually decreases from the wire surface (8 kV) to zero on the impingement surface and the bottom plate of the nozzle. Meanwhile, at the surface of the wire electrode, where ionization occurs and charge injection takes place, the charge density, ρe, and electric field strength, E, are large in the vicinity of the wire electrodes and decreases sharply in the region away from the electrodes, as depicted in Figs. 6(b) and 6(c). It is also noted that the electric field strength starts to increase as approaches the ground electrode. Additionally, due to the superposition of electric fields by every single electrode, it is necessary to solve the multiple electrode system simultaneously, in order to account for the interaction effects.

Fig. 6
(a) Electric potential distribution, (b) space charge distribution, and (c) electric field strength at an applied potential of 8 kV for an ionic wind-assisted SJR nozzle flow
Fig. 6
(a) Electric potential distribution, (b) space charge distribution, and (c) electric field strength at an applied potential of 8 kV for an ionic wind-assisted SJR nozzle flow
Close modal

The flow field for a regular SJR nozzle is shown in Fig. 7(a). The air flow, with an average velocity of 3 m/s (Re = 1624), exits the nozzle, redirects its direction with an exit angle of 20 deg, and reattaches on the surface to form a reattachment zone. Negative pressure exists in the recirculation zone, due to the entrainment of the SJR flow. This fluid flow motion agrees with the previous work by Narayanan et al. [8]. With the introduction of the corona discharge, ionic flow is generated, which impinges on the impingement surface, spreads outwardly, and recirculates within the recirculation zone, as depicted in Fig. 7(b).

Fig. 7
Comparison of air flow fields for (a) regular SJR nozzle and (b) ionic assisted SJR nozzle with 8 kV applied potential at Re = 1624
Fig. 7
Comparison of air flow fields for (a) regular SJR nozzle and (b) ionic assisted SJR nozzle with 8 kV applied potential at Re = 1624
Close modal

Figure 8 shows the comparison of pressure coefficients, Cp, on the impingement surface between a regular SJR nozzle and an ionic wind-assisted SJR nozzle. The pressure coefficient is a nondimensional parameter, based on the exit conditions of the SJR flow, i.e., Cp=P0.5pv02. For the regular SJR nozzle, due to the redirection of the outflow, the peak pressure coefficient, Cp = 0.88, occurs at the reattachment zone (x = 28.4 mm). On the impingement surface, underneath the bottom plate in the recirculation zone, a nearly constant negative pressure region exists; For instance, from x = 0 to x = 18 mm, Cp remains at −0.23. The negative pressure is due to the air entrainment, and the magnitude of the pressure coefficient is highly dependent on the exit angle. The reasons for this have been explained in detail in the previous work of Narayanan et al. [8]. For the ionic wind-assisted SJR nozzle, despite the peak pressure occurring at the reattachment zone, a secondary peak pressure occurs right under the bottom plate (x = 0.6 mm), which corresponds to the impingement stagnation zone of the resultant ionic flow. Note that the magnitude of the Cp by ionic wind generation is like that of the SJR flow, due to the similar flow velocity magnitude. Additionally, the peak Cp = 0.84 of the ionic wind-assisted SJR nozzle at the reattachment zone locates at x = 27.2 mm. In comparison to the regular SJR nozzle, the reattachment zone of the ionic wind-assisted SJR nozzle shifts slightly inward toward the centerline (i.e., x = 27.2 mm versus 28.4 mm), this is because the inertia of the recirculating ionic flow dominates the SJR flow in the region underneath the bottom plate. It is also worth mentioning that to avoid electric disaster (i.e., an electrical avalanche), the electric field should not exceed the breakdown limit (∼107 V/m for air [33]). Thus, the maximum ionic flow velocity is constrained below 3.5 m/s, which is at the same order as the velocity of the air exit from the SJR nozzle. Accordingly, the fluid flow and the pressure field have been significantly influenced by the inducement of ionic wind.

Fig. 8
Comparison of pressure coefficients between regular SJR nozzle and ionic wind-assisted SJR nozzle with 8 kV applied potential at Re = 1624
Fig. 8
Comparison of pressure coefficients between regular SJR nozzle and ionic wind-assisted SJR nozzle with 8 kV applied potential at Re = 1624
Close modal

Figure 9 compares local and average heat transfer coefficients between a regular SJR nozzle and an ionic wind-assisted SJR nozzle at various applied electric potentials. For the regular SJR nozzle in the absence of electric potential application (case 1), the local heat transfer coefficient remains low in the recirculation region, while reaching its maximum at the reattachment zone (i.e., at x = 28.4 mm, hloc = 56.9 W/m2·K). For the ionic wind-assisted SJR nozzle (cases 2 and 3), as expected, in the recirculation region, the induced ionic flow significantly enhances the local heat transfer coefficient. As an example, in case 2 with the application of 8 kV, at the impingement zone of ionic flow (i.e., x = 0.6 mm), hloc of the ionic flow case achieves 76.1% enhancement, compared to that of the regular SJR nozzle in case 1 (16.2 W/m2·K versus 9.2 W/m2·K, respectively). Due to the recirculating ionic wind, an additional flow, though less noticeable, is generated between the ionic flow impingement zone and the reattachment zone, i.e., at x = 15 mm, which results in a higher local Cp and a secondary peak of hloc. For instance, in case 3, at x = 15 mm, Cp and hloc are greater than those in case 1 by 62.5% and 119.2%, respectively (−0.09 versus −0.24 for Cp and 17.1 W/m2·K versus 7.8 W/m2·K for hloc, respectively). Afterward, the heat transfer enhancement diminishes along the x-axis in the absence of corona discharge. As is consistent with the shift of the reattachment zone due to the ionic flow, the peak hloc occurs closer to the symmetric nozzle centerline due to the dominance of ionic flow inertia. The impact of applied potential magnitude is also evaluated in cases 2 and 3, with the application of 7 kV and 8 kV on the wire electrodes, respectively. According to Kaptzov's hypothesis and Peek's formula, as the applied voltage exceeds the critical voltage, the electric field at the electrode surface is only a function of the electrode dimensions, rather than the variation of the electric potentials. Thus, the charge density at the electrode surface (ρe,wire) needs to be accordingly adjusted. As expected, the hloc increased with the higher applied potential in the recirculation region, while it decreases in the reattachment region, where the corona discharge diminishes.

Fig. 9
Comparison of local and average heat transfer coefficients under various applied potentials for the ionic wind-assisted SJR nozzle at Re = 1624
Fig. 9
Comparison of local and average heat transfer coefficients under various applied potentials for the ionic wind-assisted SJR nozzle at Re = 1624
Close modal

In cases 4 and 5, the comparison of average heat transfer coefficients is presented. The calculation of havg provides a better comparison of the nozzle's effectiveness. The ionic wind-assisted SJR nozzle (case 5) shows a higher havg, compared to that of the regular SJR nozzle (case 4). An enhancement of 72.1% (14.8 W/m2·K versus 8.6 W/m2·K, respectively) is achieved in an average heat transfer coefficient at the edge of the recirculation region (i.e., x = 19 mm). Taken together, the ionic wind-assisted SJR nozzle shows a superior heat transfer performance than the SJR nozzle.

The influence of the air exit Reynolds number (Re) is also investigated, as presented in Fig. 10. The definition of the Reynolds number is based on the hydraulic diameter of the SJR nozzle at the exit, which equals two times the jet exit width (2be). As the Re-increases, the peak heat transfer coefficient at the reattachment zone increases, which is due to the unique SJR flow pattern. For instance, in cases 2 and 3, as the exit velocity increases from 3 m/s to 3.5 m/s, which corresponds to the increase of the Reynolds number from 1624 to 1895, the peak hloc, occurs at x = 28.4 mm, is increasing from 54.7 W/m2·K to 61.6 W/m2·K, respectively. Meanwhile, the local heat transfer in the recirculation region is enhanced from a higher exit Reynolds number, this is because more air entrains into the recirculation region. On the other hand, at a low exit Reynolds number, i.e., Re = 541 in case 1, the hloc changes dramatically both in position and magnitude under the bottom plate of the nozzle. A single peak hloc = 58.2 W/m2·K occurs at x = 9.1 mm. This significant change of the heat transfer characteristic is due to the alteration of the SJR flow pattern at low exit velocity by the ionic flow, as illustrated in Fig. 11. At an exit velocity of 1 m/s, compared with the fluid flow of a regular SJR nozzle, the SJR flow alters in the presence of ionic wind. More specifically, in Fig. 11(b), due to the dominance of the ionic wind over the SJR flow inertia, the SJR flow coming out of the nozzle exit is attracted toward the recirculation region, rather than reattaching on the impingement surface. Then the mixing between SJR flow and ionic wind creates multiple vortices in the region under the bottom plate. Even though the low exit velocity case (i.e., Vexit = 1 m/s) may yield a higher local heat transfer enhancement, it is not desirable for the practical application, since it performs a lower average heat transfer enhancement on the overall impingement surface. For instance, the case 4 with Re = 541 experiences 28.8% lower of havg, compared to that of case 6 (23.5 W/m2·K versus 33.0 W/m2·K, respectively) at x = 70 mm.

Fig. 10
Comparison of local and average heat transfer coefficients under various exit Reynold numbers for the ionic wind-assisted SJR nozzle with 8 kV applied potential
Fig. 10
Comparison of local and average heat transfer coefficients under various exit Reynold numbers for the ionic wind-assisted SJR nozzle with 8 kV applied potential
Close modal
Fig. 11
Comparison of fluid flow fields under exit Reynold number of 541 between (a) regular SJR nozzle and (b) ionic wind-assisted SJR nozzle with 8 kV applied potential
Fig. 11
Comparison of fluid flow fields under exit Reynold number of 541 between (a) regular SJR nozzle and (b) ionic wind-assisted SJR nozzle with 8 kV applied potential
Close modal

Conclusions

Numerical simulations were conducted to evaluate the heat transfer characteristics of a novel ionic wind-assisted SJR nozzle. The combined effects of applied ionic wind electric potential and exit air Reynolds number on the fluid flow field, impingement surface pressure distribution, and the resultant heat transfer coefficients were studied. Under laminar conditions, the results showed that the induced ionic wind significantly influenced the flow field and the local and average heat transfer coefficients within the recirculation region. Furthermore, the numerical results indicated that enhancements of up to 76.1% and 72.1% in local and average heat transfer coefficients, respectively, were achieved on the impingement surface in the presence of the ionic wind. The heat transfer enhancement due to the ionic wind increased with the increase of applied electric potential but decreased with the exit air Reynolds number. Additionally, the presence of ionic wind impacted the location of peak pressure on the reattachment surface; it moved closer to the recirculation region.

Funding Data

  • United States Department of Agriculture (USDA) (Grant No. 2018-6701-27913; Funder ID: 10.13039/100000199).

  • Center for Advanced Research in Drying (CARD), a U.S. National Science Foundation Industry University Cooperative Research Center (Grant No. 1624767; Funder ID: 10.13039/100000001).

Nomenclature

Variables
b =

ion mobility, m2/V·s

be =

nozzle exit opening, mm

cp,air =

specific heat of air, J/kg·K

Cp =

pressure coefficient, Cp=P0.5pv02

D =

ion diffusivity, m2/s

dh =

hydraulic diameter of SJR nozzle, dh=2be, m

E =

electric field vector, V/m

Ew =

critical electric field strength, V/m

fe =

electric body force density, N/m3

g =

gravity acceleration, m/s2

hloc =

local convective heat transfer coefficient, W/m2·K

havg =

average convective heat transfer coefficient, W/m2·K

k =

thermal conductivity of air, W/m·K

P =

pressure, Pa

P0 =

atmospheric pressure, Pa

rw =

radius of wire electrode, mm

T =

temperature, K

T0 =

air temperature at SJR nozzle exit, K

Ts =

impingement surface temperature, K

Tamb =

ambient air temperature, K

Abbreviations
DEP =

dielectrophoresis

EHD =

electrohydrodynamic

Re =

Reynold number, Re = ρvdhμ

SJR =

slot jet reattachment

Greek Symbols
εe =

electric permittivity, F/m

μ =

dynamic viscosity of air, N·s/m2

ρ =

fluid density, kg/m3

ρe =

space charge density, C/m3

Φ =

electric potential, V

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