What is Tesla Valve? Tesla Type Valve Design How?

What is Tesla Valve? Tesla Type Valve Design How?

Highlights

Designed a new Tesla-valve that was integrated in a pulsating heat pipe.

Performed laminar single phase modelling and steady two-phase flow experiments.

The valve produces diodicity in two-phase flow.

Thermal resistance is reduced by incorporating Tesla valves in the pulsating heat pipe.

Abstract

A new Tesla-type valve is successfully designed for promoting circulation in a pulsating heat pipe (PHP) and improving the thermal resistance. Its functionality and diodicity is tested by laminar single-phase modelling and by steady two-phase flow experiments. The valve is symmetrically integrated in a single-turn PHP, which reduces variabilities to give a more thorough understanding of the behaviour in PHPs. Two transparent bottom-heated PHPs, one with and one without valves, are manufactured and the flow behaviour and thermal performance is studied. The valves produced a diodicity which lead to a difference in velocity of 25% for the different flow directions. Furthermore, a decrease of 14% in thermal resistance was observed due to the addition of the valves.

1. Introduction

The demand for faster and smaller micro-electronic systems continues to increase and consequently, the amount of produced heat per volume increases. Therefore, the need for novel efficient cooling devices is vast [1]. Heat pipes are effective passive heat spreaders that can be used to solve this problem. Due to the combined convection and phase transition, a high heat exchanging efficiency can be achieved [2]. A drawback of the traditional heat pipe is that it requires an intricate wick structure and cannot be easily miniaturised due to the capillary limit [3]. Therefore, a new heat pipe called the Pulsating (or Oscillating) Heat Pipe (PHP) was introduced by Akachi in 1990 [4]. The main benefits of the PHP are that it has a very simple shape with no wick structure, which can be easily miniaturised. This makes it a very inexpensive and easy-to-integrate heat spreader which can be beneficial for many, also non-electronic, applications [5].

A PHP generally consists of a simple meandering capillary tube or channel which alternatingly passes through evaporator (heating) and condenser (cooling) zones as schematically shown in Fig. 1. Due to the capillary size of the channel a series of liquid slugs and vapor plugs is formed by the working fluid. The constant heat exchange triggers phase-change phenomena which result in pressure variations inside the device that consequently trigger movement of the liquid slugs and plugs. The overall heat transfer is mainly determined by the sensible heat transfer and the latent heat contributes mostly to the movement of the slugs and plugs [6]. The performance of a PHP thus relies on the continuous non-equilibrium conditions throughout the system and an intricate interplay of physical phenomena. Depending on the specific conditions, the liquid slugs are stagnant, pulsating, circulating with a superimposed pulsation or purely circulating [7], [8]. Furthermore, the flow pattern can vary from the normal bubble–liquid slug flow to annular flow [9]. The PHP has received large interest in the scientific community, however, due to the complexity and chaotic behaviour, no fully comprehensive theory or model and no general design tools are available

It is known that circulation of the working fluid contributes to a better performance of the PHP [12], [13], [14]. The liquid contact in the evaporator is increased when the working fluid is circulating, which increases the heat transfer. This makes it interesting to investigate methods to promote circulatory motion in a PHP [9], [15]. Moreover, directional promotion could increase the stability and predictability of the PHP.

Circulatory motion has been induced inside PHPs using asymmetrical heating [16], floating-ball check valves [17], a variation of channel diameters [9], [18], [19] and Tesla-type valves [20]. Although being of scientific interest, promoting the circulation using asymmetrical heating is not practically applicable. Similarly, using floating-ball check valves inherently contradicts the benefits of the PHP by having a moving part and being difficult to manufacture when integrated and/or miniaturised.

A more practical solution is to utilize asymmetrical flow resistance to promote directional circulation. Holley and Faghri [18] were the first to suggest this by varying the channel diameter. It was demonstrated that this could theoretically improve a directional flow in a single-turn PHP and also improve the heat transfer. These phenomena were attributed to the fact that a bubble in an expanding channel will move in the diverging direction due to unbalanced capillary forces. When the tube diameter is varied in the condenser and the evaporator, i.e. having alternating channel diameters per turn, this effect is exploited to promote a circulatory flow. Kwon and Kim [19] performed experiments on several single-turn closed loop PHPs with a varied channel diameter. Besides the diameters, the heat input and inclination angle were also varied. It was concluded that a dual-diameter helps to generate a circulating flow at a lower input power and a maximum decrease in thermal resistance of 45% was found. Also it was shown that an optimum of diameter difference exists due to the fact that the smaller tube increases the flow resistance and therefore reduces the mass flow rate of the fluid. Liu et al. [9] performed experiments on three different PHPs with four turns of which one had alternating channel diameters and another had a single section in the adiabatic section which had a larger diameter. These modifications both induced the circulatory motion and improved the thermal performance compared to the standard PHP. Although these variations in channel diameter can promote circulatory flow significantly, the effect is substantially dependent on gravity. The bubble movement will cause the larger channel to contain more vapor than the smaller channel. This causes an unbalance in gravitational force which is the main driving force that promotes the circulating flow [19]. This influence is believed to be reduced when the overall size decreases and the number of turns increases [19], [21].

A second option of creating an asymmetrical flow resistance is to utilize flow rectification structures or ’no-moving-parts’ passive valves. Proven to function for micro-pumps, these valves have received great interest in the field of microfluidics due to the fact that they are easy to manufacture, durable and can transport fluids containing particles [22], [23]. The valves are structures that have a higher pressure drop for the flow in one direction (reverse) than the other (forward). This difference in flow resistance causes a net directional flow rate in the forward direction in oscillating flows. The efficiency is often expressed in diodicity Di, being the ratio of pressure drops for identical flow rates [24]:(1) $Di = {(\frac{Δ p_{r}}{Δ p_{f}})}_{Q}$ where $Δ p_{r}$ is the reverse flow pressure drop and $Δ p_{f}$ the forward flow pressure drop for flow rate Q. A large number of different rectifying structures exist [23], [25], but the Tesla-type valve [26] is the most promising option to apply in a PHP. It is easy to integrate, has a low additional flow resistance in the promoted direction [27] and could enhance the thermal efficiency due to additional mixing effects [28]. The difference in flow resistance of the Tesla-type valve results from the difference in flow path for the majority of the flow through the two separated channels of the valve for both flow directions [24].

Thompson et al. [20] were the first to apply Tesla-type valves in a PHP which was designed for flow visualization using neutron radiography. Eight valves were applied in the adiabatic section of a six-turn flat-plate PHP. An experimental analysis was performed and the results show that the circulation is promoted in the desired direction, and that this promotion increases with heat input. Moreover, the PHP with the Tesla-valves had a smaller thermal resistance than the standard PHP and the difference was in the order of 15–25% depending on the heat input. An additional interesting observation is that the percent-increase in thermal performance was of the same order-of-magnitude as the percent-increase of flow-directionality between both heat pipes.

In order to optimise these Tesla-type valves, a better understanding of the behaviour of a two-phase flow in the valve is needed. To the authors’ knowledge, no comprehensive research on two-phase flow in Tesla-type valves exists. For this reason, this paper provides more insight to this subject with the focus on PHP application. A new valve design is proposed of which the functionality is tested using a single-phase model and a steady two-phase flow controlled experiment. To gain better insight in the valve performance in a PHP, it is symmetrically integrated in a single-turn flat-plate transparent PHP of which the temperature and fluid motion is measured. A single-turn is used to reduce variabilities and for the reproducible behaviour. The findings can be used as building blocks for a multi-turn PHP [29], [14].

2. Valve design

A new Tesla-type valve has been developed for implementation in a PHP based on two criteria. The inlets and outlets should be aligned while maintaining a compact geometry that can be easily integrated in a PHP and the diodicity should be maximised while maintaining a low pressure drop in the promoted direction. The second criteria is based on the fact that movement in a PHP is related to pressure differences. A diodicity should thus be produced while having minimum resistance in the promoted direction. Based on these criteria and the general valve design guidelines, proposed by Bardell [24], the design shown in Fig. 2 is drafted. The dimensions of this design, referred to as the D-valve, are indicated in Fig. 2A and are given in Table 1. The left channel of the valve is referred to as the side channel and the right as the main channel. The channel junctions, indicated by the grey areas in Fig. 2B, are referred to as junctions J1 and J2. The main guidelines to improve diodicity are that the side channel should be aligned with the main channel in junction 2, such that for reverse flow a significant amount of flow enters the side channel, and that the angle of the side channel with the main channel in junction 1 is high. The current design is a trade-off between these guidelines and the above mentioned criteria, however it is not fully optimised.

Table 1. D-valve dimensions in millimetres.

Parameter	Value in mm
W	2
L1	10
L2	2
L3	8.75
L4	7.85
L5	24.65
L6	50
R	Radius 22
a	Radius 2.5 (Angle $α$ = 33°)
b	Radius 4 (Angle $β$ = 243.5°)
e	Radius 2 (Angle $∊$ = 75°)

2.1. Single-phase model description

To verify the functioning of the D-valve a laminar single-phase model is made with COMSOL [30]. It must be noted that the goal of the numerical work was not to model the performance of the valve in a PHP-type flow, but purely investigate its efficiency in a single-phase flow. Due to the high computational costs of an accurate three-dimensional model, a two-dimensional model is used to verify the mesh dependence and make a comparison with other Tesla-type valve designs in literature. Various authors state that a two-dimensional model overestimates the diodicity compared to a three-dimensional model, however 2D simulations still give a good indication of the functioning of the valve therefore making it useful for comparing geometrical variations [22], [31], [32], [33]. Since the valve will be implemented as a square channel geometry, also a 3D model is made using similar mesh settings to compute the actual diodicity. The results of this model are used to show the similarities and differences in diodicity between the 2D and 3D model and can be used to compare with experimental results. The working fluid used for the simulations is water at 20 °C. The flow is assumed to be incompressible and transient effects can be neglected for determining the diodicity, i.e. the efficiency [24]. Furthermore, isothermal conditions are considered, thus gravity effects can be disregarded. Therefore, the following Navier–Stokes and continuity equations are solved by the model:(2) $ρ (u \cdot \nabla) u = \nabla \cdot [- p I + μ (\nabla u + {(\nabla u)}^{T})]$ (3) $ρ \nabla \cdot (u) = 0$

The geometry shown in Fig. 2 is meshed with a free-tetrahedral mesh with refinement of the mesh where large velocity gradients are expected, i.e. near channel junctions and the walls. Mesh independence was verified with the 2D model, using the same criteria as Gamboa et al. [31], i.e. by doubling the number of elements starting with a coarse mesh until the solution changed less than 4%. This resulted in a mesh of 44,000 elements for the 2D model and 1260,000 elements for the 3D model.

A forward and reverse flow case is studied for a range of Reynolds numbers. The Reynolds number is defined as $Re \equiv ρ D_{hyd} u / μ$ with $ρ$ the fluid density, $D_{hyd}$ the hydraulic channel diameter, u the characteristic fluid velocity and $μ$ the fluid viscosity. The Re of the liquid slugs in a PHP can be of an order of $10^{2}$ to $10^{3}$ [29], but Thompson et al. [32] indicate that transitional flow behaviour can exist in a 3D Tesla-type valve for $Re ≳ 300$ . The modelled Re range is therefore determined by the convergence of the model, i.e. the part where pure laminar flow exists. In forward flow the bottom boundary is set as the inlet and the top boundary as the outlet, both indicated with I/O in Fig. 2. This is the other way around for reverse flow. At the inlet, a laminar inflow condition is applied using an entrance length to have a fully developed inlet flow [34]:(4) $l = 0.056 \cdot D_{hyd} \cdot {Re}_{in}$ where ${Re}_{in}$ is the Reynolds number based on the average inlet velocity and hydraulic diameter. A zero pressure condition is applied at the outlet. The other boundaries (solid black lines in Fig. 2) have a no-slip boundary condition. The symmetry of the problem is used by applying a symmetry and no-slip boundary condition at the additional symmetry plane and bottom boundary of the 3D model respectively. Thus, only a 1 mm deep geometry, corresponding to a hydraulic diameter of 2 mm, has to be solved which saves computation time. For the 2D model a direct PARDISO solver is used and for the 3D model an iterative GMRES solver. The relative tolerance is $10^{- 3}$ . The pressure drop in each direction is calculated by evaluating the average pressure on the evaluation lines/surfaces, indicated with P1 and P2 in Fig. 2B. Computing the pressure drop for each flow direction and dividing these results in the diodicity for the corresponding Reynolds number.

2.2. Valve characteristics

A surface plot of the velocity magnitude, plotted in grey-scale, obtained by the 2D model in both directions for $Re = 200$ is shown in Fig. 3. Reverse flow is shown on the left and forward on the right. Furthermore, uniformly positioned streamlines and the velocity field on four lines, indicated by arrows, are also plotted. As mentioned, the working principle of a Tesla-type valve is based on a difference in flow distribution between both flow directions, which results in a difference in pressure drop for the same inlet flowrate. When the pressure drop would be identical for both directions, this will result in a difference in flowrate. As can be seen in Fig. 3, 83% of the flow goes through the main channel in the forward case while 55% goes through the main channel in the reverse case. This difference in distribution is dependent on the inertia of the flow and therefore inherently increases with Re. The flow through the side channel has to be redirected downstream, which requires significant pressure work. When combined with the main channel flow, it also creates a high shear region in junction 2. For the laminar range, these are the main sources of diodicity in a Tesla-type valve [24].

As shown in Fig. 3, a clear recirculation zone exists in the side channel for the forward case resulting in a small separated jet. This jet shows to be more pronounced in 3D. The 2D forward case does not converge for $Re > 650$ , while the reverse case is still converging. With only the forward case of the 3D model not converging for $Re > 200$ , this phenomena is believed to result in transitional flow behaviour causing the non-convergence of the laminar model. The diodicity up to $Re = 200$ of the 2D and the 3D model is shown in Fig. 4, indicating the difference between an infinitely deep and a square channel.

To verify the performance of the developed valve the geometric values of several other valve designs are copied from literature, scaled to the same channel size and implemented in the 2D model. Scaling the valves has no influence on the relation between the Reynolds number and the diodic performance in single-phase laminar flow [27]. The same inlet length (L1 in Fig. 2A) and pressure evaluation distance (L2 in Fig. 2A) is used for all the designs. A distinction can be made between the normal Tesla valves used for micro-pump application and the Tesla valves for PHP application. The integration of the alignment of the inlets into the valve geometry does reduce the maximum diodic potential of the valve. The computed single-phase diodicity of the different designs is shown in Fig. 5 with the valve designs indicated in the legend. The micro-pump valves are the traditional T45A valve (square marker) [24], the T45C valve (asterisk marker) [24] and the GMF valve (circle marker) [31]. The T45C valve and GMF valve are the result of improvements by Bardell [24] and an optimisation study performed by Gamboa et al. [31] on the traditional Tesla-valve respectively. The fourth design (triangle marker) is the design which was already applied in a PHP by Thompson et al. [20] referred to as the TMW valve. The TMW valve only converged for $Re \leq 250$ . However, when comparing the TMW valve with the proposed new D-valve, both designed for PHP application, it can be clearly observed that the D-valve design produces a higher diodicity than the TMW design. Due to the difference in inlet and outlet alignment and path-length between the different designs a better comparison of effectivity is based on the absolute pressure difference between reverse and forward flow, which is shown in Fig. 6. This proves that the proposed D-valve design is a properly performing Tesla-type valve, having an absolute pressure difference close to the T45C valve which is very promising especially concerning that the alignment of the inlets and outlets is incorporated in the design. The GMF valve results show the potential of a full geometrical optimisation, which could still be performed on the developed geometry.

The single-phase modelling illustrated the basic functioning of the developed valve in single-phase flow. Furthermore, the comparison with other Tesla-type valves from literature showed that the new design is a proper functioning Tesla valve in single-phase flow that can be easily integrated in a PHP. However, the final implementation of the valve will be in a two-phase flow with heat transfer. Modelling this flow is very complex and time-expensive, therefore it is chosen to be studied experimentally.

3. Experimental set-up and procedure

To identify the operational characteristics of the D-valve in PHP-type flow, two experiments are performed. First a steady liquid–gas slug-plug flow through the valve is studied with the ‘two-phase experiment’. Secondly, the valve is integrated in a single-turn PHP, where the diodic performance of the valves and the effects on the motion composition and thermal performance of the PHP are studied.

3.1. Two-phase experiment

To the authors’ knowledge, no research on the functioning of a Tesla valve in two-phase flow has been performed. To study this, a test device is developed with which a steady liquid–gas flow though the D-valve can be observed. The goal of this experiment is to identify the behaviour of the valve in two-phase flow and verify whether diodicity is produced. The test device is schematically shown in Fig. 7. It comprises out of two 140 × 40 ${mm}^{2}$ transparent PMMA plates. A square 2 mm deep channel, illustrated by the dashed line pattern in Fig. 7, is milled into the 4 mm thick bottom plate. The channel cross-section relates to a commonly used hydraulic diameter for water filled PHPs [11]. Related to the Bond number, which is a dimensionless number characteristic for the importance of surface tension forces to body forces, this hydraulic diameter is small enough for the water to naturally form liquid slugs and vapor plugs. This is essential for the PHP to be functional and is governed by:(5) $D_{hyd} ⩽ 2 \sqrt{\frac{γ}{g (ρ_{l} - ρ_{v})}}$ where $γ$ is the surface tension, g the gravitational constant, $ρ_{l}$ the liquid density and $ρ_{v}$ the vapor density of the working fluid [10], [35].

Holes for the liquid inlet (IL), gas inlet (IG), outlet one (O1) and outlet two (O2) are made the 1 mm thick top plate using a laser-cutter. Double-sided adhesive tape (thickness ∼0.1 mm), with the dashed line pattern cut-out, is used to bond the two plates together.

The working fluid is water dyed with blue food colourant (BPOM RI MD. 263109077128) for contrast with a ratio of 125:1. Ambient air is used as the working gas. Both the working fluid and gas had a temperature of 22 °C. The water and air are simultaneously pumped with a 1:1 volume ratio into the inlets by a syringe pump (Nexus 3000) using 50 ml syringes. Thereby, a perfectly slug-plug alternating flow is created with slug and plug lengths between 2 and 3 mm as illustratively shown in Fig. 7. The initial meandering channel is added to reduce fluctuations in the flow by increasing the total flow resistance of the device. By closing-off one of the two outlets the direction of flow through the valve can be chosen. To quickly attain a steady-state flow and diminish the effect of initial distribution, the device is first shortly flushed with a high flow rate after which the flow rate is instantly reduced to the required value. Due to

What is Tesla Valve? Tesla Type Valve Design How?