WO2015049647A1 - Diffuser - Google Patents

Abstract

This invention concerns a diffuser (50, 80, 100). The diffuser (50, 80, 100) includes an inlet (52, 82, 102), an outlet (54, 84, 104) and a diverging flow channel located between the inlet and outlet. The channel has a side wall (66.1, 66.2, 86.1, 86.2, 106) of which at least a portion diverges at a divergence angle (Θ). A bank (68 94, 114) of elements (70, 96, 116) is located at least partially inside the flow channel so that the elements are in the fluid flow path between the inlet (52, 82, 102) and outlet (54, 84, 104). In the preferred embodiment the elements are arranged such that they are staggered in the nominal stream-wise direction 72 but are linearly aligned along the diverging portion of the side wall (66.1, 66.2, 86.1, 86.2, 106) of the flow channel. The fluid momentum along the boundary wall is, in use, increased as a result of the aligned elements (70, 96, 116) along the side wall (66.1, 66.2, 86.1, 86.2, 106) of the channel and a static pressure drop is, in use, induced through the dispersion of fluid by the staggered elements in the stream-wise direction. The diffuser (50, 80, 100) reduces boundary layer separation to achieve substantially uniform flow velocity at an outlet (54, 84, 104) of the diffuser.

Description

D!FFUSER

BACKGROUND TO THE INVENTION

This invention relates to a diffuser. In particular, but not exclusively, the invention relates to a diffuser for use in regulating fluid flow characteristics of a fluid supplied to a filtration device, such as an electrostatic precipitator, for example.

Effluent gases produced during power generation often contain particulates, typically in the form of suspended particles of liquid or solid, which are a recognised risk to human health and the environment. Therefore, a variety of gas-cleaning processes have been developed to remove particulates from effluent gases. Amongst the most common technologies is electrostatic precipitation [1]. To function effectively, an electrostatic precipitator (ESP) requires low-velocity, uniform flow of effluent gases, which can be achieved with the use of a diffuser upstream of the ESP [2]. However, a diffuser is inherently vulnerable to boundary layer separation [3]. Figure 1 shows a known diffuser 200 in which the boundary layer has separated. The divergence angle Θ is indicated, along with the inlet area and outlet area A₂ of the diffuser. Flow is confined by the separated boundary layer, resulting in a core jet 202 through the centre of the diffuser. Consequently, flow downstream of the diffuser is neither low-ve!ocity nor uniform, which adversely affects ESP performance.

Boundary layer separation occurs inside a diffuser because fluid momentum in the boundary layer is overcome by an adverse pressure gradient. Boundary layer separation can therefore be prevented by two means, namely by reducing the adverse pressure gradient and by increasing fluid momentum in the boundary layer. Both methods have been separately explored for a diffuser, by previous studies [4, 6-9, 11-27].

To reduce the adverse pressure gradient, the reasons for its existence must be understood [4]. First, a convex corner 204 at and inlet 206 of the diffuser causes sudden changes in fluid velocity that must result in an adverse pressure gradient [5]. Second, divergence of the diffuser walls 208 leads to static pressure recovery, which also generates an adverse pressure gradient. It has been suggested to reduce the pressure gradient by rounding the inlet corners 204 [4] or adding curvature to the diffuser walls 208 [6, 7], However, it has been found that these methods are not as effective in reducing the pressure gradient as reducing the divergence angte Θ of the diffuser [8]. Gradual divergence, i.e. a reduction in the divergence angle Θ is not always suitable as it conflicts with spatial constraints. The area ratio (A2/A1) of an ESP diffuser typically ranges between 10 and 20 [2, 9], which results in a long diffuser if the divergence angle Θ is small. In applications where compactness is a priority, a wide- angie diffuser design must be used, resulting in a strong adverse pressure gradient.

As mentioned above, the second means of preventing boundary layer separation is to increase fluid momentum in the boundary layer. Increasing near-wa!l fluid momentum can be accomplished by a variety of methods, with or without the use of auxiliary power [10]. Methods which require no auxiliary power, aiso referred to as passive methods, include the use of vortex generators [11], guide-vanes [12-14], splitter plates [15-16] and screens [7]. On the other hand, methods which require auxiliary power, also referred to as active methods, include the use of moving walls [ 7], suction [18] or blowing [19] techniques. Ail of these approaches have been previously applied to a diffuser, with a comprehensive review by Mehta [20].

Amongst these methods, screens are acknowledged as the predominant technology in wide-angle diffuser designs [20], primarily due to the achievable flow uniformity [21]. Screens cause substantial total pressure loss within a diffuser, but wide-angle diffusers are not intended toward pressure recovery [20]. An ESP diffuser prioritises flow uniformity and compactness above all else; hence screens are commonly applied [2] with extensive optimisation by numerous studies [9, 22-27].

The mechanism by which screens increase fluid momentum near the wall of the diffuser is an "impingement" effect, whereby flow encountering the screen is splayed out towards the diffuser wails, thereby reducing boundary layer thickness and consequently suppressing separation [7]. However, one disadvantage of using a screen is that it can only prevent separation within a limited stream-wise vicinity. The stream-wise is the direction of the stream of material or fluid flow on entry to the diffuser. In view of this disadvantage a wide-angle diffuser often requires multiple screens. Determining the number of screens required, as well as the stream-wise location and porosity, i.e. open-area, of each screen is a substantial design effort. Guidelines do exist to assist with such designs [20], but the specific geometry of the particular diffuser wiii always determine the optimal configuration. A long-standing issue with screened diffusers is structural integrity [20, 27, 28]. For example, wire-gauze screens strain in high- velocity flow and can become clogged with particulates. As a result, wire- gauze screens require regular maintenance [20]. Screens of perforated plate on the other hand have been found to be abraded [27, 28] in use. Screens of perforated plate are vulnerable to wear because the sudden reduction in flow area can lead to high local velocities through the plate apertures, which promotes erosion. Although screens may be used to prevent boundary layer separation in an ESP diffuser, this solution is not ideal as it is design and maintenance intensive.

In view of the above it is evident that the current methods suggested to prevent boundary layer separation have several drawbacks. As mentioned above, gradual divergence of the diffuser conflicts with spatial constraints and screened diffusers are design and maintenance intensive. Furthermore, the current methods each only incorporate one of the abovementioned two means by which boundary layer separation can be suppressed, in other words, the current methods target either the pressure gradient or the fluid momentum in the boundary layer but not both.

It is an object of this invention to alleviate at least some of the problems experienced with existing diffusers and, in particular, wide-angle diffusers. it is a further object of this invention to provide a diffuser and method that will be useful alternatives to existtng diffusers and methods for reducing boundary wall separation, it is yet a further object of the invention to provide a diffuser and method for reducing boundary layer separation inside a wide-angle diffuser by reducing the adverse pressure gradient while increasing near-wall fluid momentum.

SUMMARY OF THE INVENTION

In accordance with the invention there is provided a diffuser having an inlet and outlet, the diffuser including:

a diverging flow channel located between the inlet and outlet, the channel having a side wall of which at least a portion diverges at a divergence angle; and a bank of element located at least partially inside the flow channel so that the elements are in the fluid flow path between the iniet and outlet, at least some of the elements being arranged such that they are staggered in a nominal stream-wise direction but are linearly aligned along the diverging portion of the side wall of the flow channel,

wherein fluid momentum along the boundary wall is, in use, increased as a result of the aligned elements along the side wall of the channel and a static pressure drop is, in use, achieved through the dispersion of fluid by the staggered elements in the stream-wise direction, thereby reducing boundary layer separation to achieve substantially uniform flow velocity at an outlet of the diffuser.

The porosity of the bank of elements, i.e. the volume of the element bank unoccupied by elements, may be between about 0.9 and about 0.99, preferably between about 0.950 and about 0.99, and more preferably about 0.989.

The elements in the bank may be arranged in an equilateral triangle unit cell.

The elements may be in the form of cylinders which run substantially parallel to one another. The cylinders are preferably circular in cross- section.

In one embodiment of the bank of elements includes multiple rows, preferably about 20 rows, of cylinders distributed along the nominal stream- wise flow direction. Each row of cylinders preferably has one more cylinder than the preceding row.

In one embodiment of the invention, the bank includes between about 350 and 400 cylinders. The bank may include about 390 cylinders.

In another embodiment of the invention the diffuser may include a second bank of cylinders, wherein the diverging channel diverges tn two planes which are substantially perpendicular to each other, and wherein the first and second banks of cylinders are arranged substantially perpendicular to one another so that the cylinders of the first banks run substantially perpendicularly to the cylinders of the second bank, such that the fluid flow is dispersed in both planes of divergence.

The cylinders of the first and second cylinder banks may be provided in coincidental planes so that they are collapsed onto each other to form gridlike structures. The planes in which the cylinders of the first cylinder bank run may be separated in the stream-wise direction from the planes in which the cylinders of the second cylinder bank run.

In this embodiment which includes two perpendicular banks of elements, the porosity of the combined bank of elements may be about 0.98.

In yet another embodiment of the invention the bank of elements includes a set of concentric elements of varying diameter. The concentric elements may be in the form of rings which are arranged such that the outermost rings are in-line with an internal surface of the diffuser, and the inner rings are staggered in the stream-wise direction, so that flow is channelled along the divergent conical surface and dispersed away from the diffuser axis, resulting in approximately uniform flow velocity at the diffuser outlet.

In accordance with a second aspect of the invention there is provided a method of improving the uniformity of the fluid flow velocity of a diffuser including an inlet, an outlet and a diverging flow channel located between the inlet and outlet, the channel having a side wall of which at least a portion diverges at a divergence angle, the method including the following steps:

providing a bank of elements located at least partially inside the flow channel so that the elements are in the fluid flow path between the inlet and outlet; dispersing the flow of fluid with respect to a nominal stream-wise direction in order to induce a static pressure drop across the bank of elements; and

allowing linear flow of fluid along a boundary wali of the diverging portion of the channel to increase fluid momentum along the boundary wall; thereby reducing boundary layer separation to achieve substantially uniform flow velocity at an outlet of the diffuser.

The method may include dispersing the fluid flow in two planes of divergence by providing a second bank of cylinders, wherein the first and second banks of cylinders are arranged substantially perpendicular to one another so that the cylinders of the first banks runs substantially perpendicularly to the cylinders of the second bank.

There is provided for the method to be carried out using the diffuser according to the first aspect of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in more detail, by way of example only, with reference to the accompanying drawings in which:

Figure 1 shows a cross-sectional plan view of a prior art diffuser;

Figure 2(a) shows a cross-sectional plan view a test diffuser according to the invention in which a cylinder bank is visible;

Figure 2(b) shows a cross-sectional top view of the diffuser of Figure

2{a);

Figure 3 shows a schematic illustration of a computational mode! of the diffuser of Figure 2(a) used during experimentation; Figure 4 shows computational optimisation of cylinder bank porosity of the diffuser of Figure 2(a);

Figure 5 shows the downstream velocity profiles for an empty diffuser

(ε = 1);

Figure 6 shows the downstream velocity for a cylinder bank with a low porosity (ε = 0.73);

Figure 7 shows the downstream velocity for a cylinder bank with a high porosity (ε = 0.99);

Figure 8 shows a schematic illustration of the aerodynamic anisotropy of the cylinder bank of the diffuser of Figure 2(a);

Figure 9(a) shows an endwali flow visualisation of the global flow distribution through the cylinder bank of the diffuser of Figure 2(a);

Figure 9(b) shows an endwali flow visualisation of the flow around a single cylinder of the cylinder bank of the diffuser of Figure 2(a);

Figure 9(c) shows a schematic illustration of the endwail flow visualisation of Figure 9(b);

Figure 10 shows the experimental static pressure distribution along a side wall of the diffuser of Figure 2(a);

Figure 11(a) illustrates a fluid flow profile of an excessive porosity regime;

Figure 11(b) illustrates a fluid flow profile of a deficient porosity regime; Figure 11{c) illustrates a fluid flow profile of a critical porosity regime;

Figure 12 shows a perspective view of a pyramidal test diffuser in accordance with the invention;

Figure 13 shows a cross-sectional view of the pyramidal diffuser of

Figure 12;

Figure 14 shows a cross-sectional end view of the pyramidal diffuser of

Figure 12;

Figure 15 shows the velocity profiles downstream of the pyramidal diffuser of Figure 12 at a transverse plane B visible in Figure 13;

Figure 16 shows a perspective view of a diffuser in accordance with a first embodiment of the invention;

Figure 17 shows a cross-sectional plan view of the diffuser of Figure

16 in which its cylinder bank is visible;

Figure 18 shows a side view of the diffuser of Figure 16 in which the orientation of the cylinders of the cylinder bank is visible;

Figure 19 shows a perspective view of a pyramidal diffuser in accordance with a second embodiment of the invention;

Figure 20 shows a cross-sectional plan view of the pyramidal diffuser of Figure 19 in which its cylinder bank is visible;

Figure 21 shows an end view of the pyramidal diffuser of Figure 19;

Figure 22 shows a perspective view of a conical diffuser in accordance with a third embodiment of the invention; Figure 23 shows a cross-sectional plan view of the conical diffuser of Figure 22; and

Figure 24 shows an end view of the conical diffuser of Figure 22.

EXPERIMENTAL TESTING AND RESULTS

Referring to Figures 2(a) to 15, in which like numerals indicate like features, two embodiments of test diffusers in accordance with the invention is generally indicated by reference numerals 10 and 40 respectively. The test diffusers 10, 40 were used during experimental testing and experimentation.

Configuration

The diffuser 10 is a wide-angle diffuser and has a cylinder bank 12 which includes a number of individually spaced apart cylinders 14. In Figure 2(a) it can be seen that the cylinders 14 are arranged periodically in cross flow.

The diffuser 10 illustrated in Figure 2(a) is in the form of a wide-angle divergent flow channel which is in fluid connection with rectangular conduits or ducting 16 and 18 respectively of constant cross-section. The ducting 16 is also referred to as the iniet ducting while the ducting 18 is also referred to as the outlet ducting. The diffuser 10 has a divergence angle Θ of 30° in the x-y plane as shown in Figure 2(a). In other words the diffuser 10 diverges with an included angle 2Θ of about 60° in the x-y plane. The diffuser 10 is of constant height H in the x-z plane, as shown in Figure 2(b). Accordingly, the diffuser 10 only diverges in a single plane, i.e. the x-y plane, and is, therefore, said to have a two-dimensional configuration. The diffuser 10 together with the inlet ducting 16 and outlet ducting 18 form the experimental test setup or rig 20 used during testing. The inventors have identified that that porosity of the cylinder bank 12 is a crucial parameter affecting boundary layer separation and flow uniformity of the fluid flowing through the diffuser 10. During experimental testing, optimisation of the porosity of the cylinder bank 12 was first performed for the two-dimensional wide-angle diffuser 0 and the results were thereafter extended to a three-dimensional test pyramidal diffuser 40 in accordance with a second embodiment of the invention described below.

Returning to the first embodiment of the test diffuser 10, it has an inlet 22 of width Q, an outlet 24 of width O, a length L, a height H and a side wall 26 of length W. The dimensions of the test rig 20 used during experimental testing are given in Table 1 below.

Table 1 : Section Parameter of Diffuser 10

The cylinder bank 12 is carefully configured and includes 390 circular cylinders 14 arranged in an equilateral triangle unit cell as shown in the detailed view of Figure 2(a). The cylinders 14 are staggered in the nominal stream-wise flow direction, i.e. the flow direction indicated by the numeral

28 along the x-axis, and arranged in-line with one another along the diffuser sidewalls 26. In this first embodiment of the diffuser 10 there are 20 rows of cylinders 14 distributed along the nominal flow direction 28, i.e. the x-axis. The first row of cylinders nearest to the inlet 22 contains 10 cylinders and each subsequent row contains one more cylinder than the preceding row. For the sake of clarity, in this configuration of cylinders 14 the last row has

29 cylinders, in the cylinder bank 12 the cylinders 14 are fixed. In view of the fact that the distance S between cylinder centres is fixed, the porosity ε of the cylinder bank 12 is expressed as a function of cylinder diameter d [29].

It is noteworthy that a change in cylinder bank porosity does not constitute the addition or removal of cylinders 14. Nor does it constitute a change in the position of the cylinders 14. The diameter d of the cylinders 14 alone is varied. The detailed parameters of the cylinder bank 12 are listed in Table 2 below.

Parameters

Optimisation of the cylinder bank porosity was initially performed for the two-dimensional configuration of the cylinder bank 12 using computational fluid dynamics (CFD). Representative cases were thereafter validated experimentally. The geometry of the dtffuser 10 and the Reynolds number (Reo) were fixed and the porosity of the cylinder bank 12 alone was varied. For each case, flow uniformity downstream of the diffuser 10 was considered, as well as the static pressure distribution along the diffuser side wall 26 which indicates susceptibility to boundary layer separation. Endwall flow within the diffuser 10 was visualized and used to explain the flow distribution.

Reynolds Number

The characteristic length of the Reynolds number (Re_Q) is the width of the diffuser inlet Q [3], and the characteristic velocity is the mean stream-wise velocity at the diffuser inlet {at traverse plane I in Figures 2(a) and (b)):

(2)

where v denotes the kinematic viscosity of air. A fixed Reynolds number of 3(10⁴) was considered for the two-dimensional configuration of the cylinder bank 12. A diffuser for an ESP generally operates at a higher Reynolds number, but flow regime is weakly affected by Reynolds number for R_eQ > 10⁴, particularly if the diffuser geometry is severe.

Inlet Boundary Layer Condition

It is known that the thickness of the inlet boundary layer can also affect performance of the diffuser 10. For example, a thin boundary layer delays separation. However, the effect is less significant for severe diffuser geometries, which are prone to severe stall irrespective of the inlet boundary layer condition [3], A diffuser for an ESP is also unlikely to encounter a thin boundary layer in use due to the substantial development length which usually precedes the device. No effort has, therefore, been made to produce a thin boundary layer at the diffuser inlet - the measured displacement thickness (26*/Q) of 0.1 is slightly less than fully developed turbulent channel flow with a 1/7 power velocity profile (25*/Q = 0.125).

Flow uniformity downstream of the diffuser

The primary measure of efficacy for a wide-angle diffuser applied to an ESP is flow uniformity, determined by velocity profiles downstream of the diffuser (at traverse plane El in Figures 2{a) and (b)}. A range of cylinder bank porosities have been numerically simulated, with experimental validation of representative cases. Velocity profiles were measured along the centre-plane, i.e. the x-y plane of Figure 2(a), of the diffuser 10 using a Pitot probe in conjunction with a multi-channel differential pressure transducer (not shown in the drawings).

The uniformity of the velocity profiles is quantified using the root mean square percentage (RMS%) [9], defined as:

where U is the mean stream-wise velocity of the profile and U_ms is the root mean square velocity, defined for a set of equally spaced data points as:

where n is the total number of data points, and u, is the local stream-wise velocity measured at position /.

A perfectly uniform velocity profile exhibits an RMS% of zero while all other conditions will produce an RMS% greater than zero. The validity of this statistic as an indicator of ESP performance has been questioned [28]; however, as a measure of flow uniformity, RMS% has been employed by several related studies [9, 22, 26], and is used here for the sake of comparison.

Static pressure distribution along the diffuser sidewail

The pressure gradient along the diffuser side wall 26 indicates susceptibility to boundary layer separation. The pressure distribution is generalised with a static pressure coefficient (C_p):

where p^ is the static pressure at the diffuser inlet 22 (traverse plane i in Figure 2); p is the fluid density and p is the local static pressure at the point where C_p is being defined.

For experimental validation of the numerical results, static pressure tappings 30 were placed on the side wall 26 of the diffuser 10 of the first embodiment shown in Figure 2(a). The tappings 30 were placed along the centre-plane of the diffuser 10, i.e. the x-y plane. As shown in Figure 2(a), five tappings were distributed evenly on the ducting 16 before the diffuser 10 and another five on the ducting 18 after the diffuser portion. Sixteen tappings were distributed evenly along the side wall 26 of the diffuser 10. A multi-channel differential pressure transducer (not shown in the accompanying drawings) was used to record pressure data.

End wail flow visualisation

The inventors used an oi!-dye technique to provide end wall flow visualisation within the diffuser 10. Fluorescent dye was mixed with light diesel oil and the mixture was painted onto the end wall. Overpassing flow shears the mixture and gradually evaporates the oil, causing dye to coagulate along time-averaged streamlines. The viscosity of the mixture was controlled by the dye-to-oil ratio, which can be optimised through trial- and-error. Ultraviolet light was used thereafter to visualise the time- averaged flow-field.

Numerical Simulation

Flow uniformity downstream of the diffuser 10 is determined by the porosity of the cylinder bank 12. A range of cylinder bank porosities have been numerically simulated for the two-dimensional configuration, using the commercial package AN SYS Fluent version 14.5. Numerical simulations have been used to identify representative porosity cases, limiting the number of necessary experiments. General

Simulations were performed at steady-state to resolve the time-averaged flow field. A pressure-based solver was employed because low air speed renders compressibility effects negligible. Temperature effects were also ignored and, therefore, air density and viscosity were fixed throughout the domain. Fluid properties were evaluated at the pressure and temperature conditions of the measured boundary conditions imposed on the domain. A coupled pressure-velocity algorithm was used, exclusively in combination with second-order accurate methods in space. Iterative convergence was monitored with the standard deviation of the downstream velocity profile and normalised residuals concerned with continuity, momentum and the turbulence model equations. Standard deviation values were required to stabilise within 0.01% and all normalised residuals were required to decline by at least four orders of magnitude before stopping the solution.

Fluid domain

Simulations were performed with a planar fluid domain, to approximate the centre-plane (x-y plane) of the diffuser, which implicitly assumes a two- dimensional fiow-fieid. Flow through the cylinder bank 12 has been experimentally observed to be three-dimensional, leading to a discrepancy in flowrate between the numerical and experimental velocity profiles measured downstream of the diffuser 10. A maximum discrepancy in flowrate of 15% was encountered, calculated with numerical integration of the velocity profiles using Simpson's rule. Despite the discrepancies in flowrate, the numerical and experimental values for RMS% agree closely.

Boundary conditions

A schematic of the domain is depicted in Figure 3, indicating boundary conditions. An experimentally measured velocity profile was imposed at the inlet to the domain at traverse plane I in Figures 2(a) and (b). The measured inlet velocity profile was found to be largely insensitive to the contents of the diffuser 10, allowing it to be used as a generic boundary condition for all simulations. 55 experimental data points were imposed across the inlet boundary. The domain is also bounded by a symmetry plane and an impermeable sidewall; flow exits the domain to measured ambient pressure conditions.

Meshing

A detaii view of the mesh is also shown in Figure 3. The diffuser 10 is discretised into unstructured triangles, due to the complex geometry of the cylinder bank 12. The inlet and outlet are discretised into structured quadrilaterals. The inflation layers lining the diffuser side wail 26 and the cylinders 14 surfaces result in y+ values [30] always less than 1. All boundary layers are spanned by at least 15 cells, in accordance with the recommendations of literature [31 , 32].

Discretisation uncertainty

Numerical uncertainty due to the global grid resolution was estimated with the Least Squares Grid Convergence Index (LSGCi) [33], regarded amongst the most reliable indicators of discretization uncertainty [34]. Each porosity case employed at least four grids. Successive grid refinement always reduced edge sizing by a factor of at least 1.3. Discretization uncertainty is indicated with error bars in the appropriate figures.

Turbulence modelling

A variety of Reynolds-Averaged Navier-Stokes (RANS) turbulence models have been applied to a cylinder bank in crossflow. Omega-based models are generally more successful within the developing-flow region of the first few cylinder rows. Epsilon-based models perform better for the developed flow region thereafter [35]. The cylinder bank 12 contained within the two- dimensional diffuser 10 comprises of 20 rows, which is sufficient to negate the entry effect of the first few rows [36]. Hence, the Realisable -ε turbulence model was employed, in combination with the Enhanced Wall Treatment recommended for low y+ values [31].

Optimisation

Flow uniformity downstream of the two-dimensional diffuser 10 was optimised by numerical simulation of various cylinder bank porosities. Representative cases in the optimisation were analysed and experimentally validated, separately.

The results of the numerical optimisation are shown in Figure 4. The ordinate is the RMS% of the downstream velocity profile at traverse plane IE in Figures 2(a) and (b), which quantifies the deviation from uniformity (see equation (3)) and the abscissa is the porosity ε of the cylinder bank 12 occupying the diffuser 10. in common practice, a velocity profile with an RMS% less than 15 is considered highly uniform [9]. Error bars for the RMS% are based on numerical uncertainty due to discretization, estimated with the LSGCi method [33].

Figure 4 demonstrates that an empty diffuser (ε = 1.00) exhibits highly nonuniform flow. The introduction of a low porosity (0.73 < ε≤ 0.88) cylinder bank provides little improvement. A high-porosity cylinder bank (0.88 < ε≤ 0.98), however, leads to a substantial improvement in flow uniformity. The eventual introduction of an ultra-high porosity (0.98 < ε < 0.99) cylinder bank produces exceptional flow uniformity, well within the acceptable limits of an ESP [9]. Optimal performance is achieved at a remarkably high porosity of 0.99, suggesting that only 1% of the diffuser need be blocked with cylinders to achieve uniform flow.

Analysis

Cases selected for independent analysis and experimental validation include the extreme cases of an empty diffuser (ε = 1.00), a low-porosity (ε = 0.73) banked diffuser and an optimal configuration of an ultra-high porosity (ε = 0.99) banked diffuser. Figures 5 to 7 show the comparison of the numerical and experimental velocity profiles downstream of the diffuser for the empty diffuser, the low-porosity banked diffuser and the ultra-high porosity banked diffuser respectively. Local stream-wise velocities u are normalised by the mean stream-wise velocity U at the diffuser inlet 22.

The traverse distance y is normalised by the diffuser outlet width O. Only half of the channel (0.0≤ y/O<0.5) is shown because of symmetry. The RMS% associated with each profile is indicated. The maximum experimental uncertainty of any u/Q_\ value is ±0.02, estimated with a method reported in Hoiman [37]. Numerical uncertainty due to discretization [33] is indicated with error bars.

Em ty diffuser

Figure 5 depicts the downstream velocity profile for an empty diffuser (ε = 1.00). Boundary layer separation occurs at the diffuser inlet, which results in a core jet through the centre of the diffuser (0 < y/O < 0.2). The peak velocity of the core jet is as high as the inlet velocity U_x , indicating negligible flow diffusion. Reversed flow occupies the diffuser periphery (0.3 < y/O < 0.5). The experimental profile does not capture the region of reversed flow because of the error associated with measuring fluctuating pressures using a Pitot probe in a region of unknown flow direction [38], The remainder of the profile shows good agreement between the numerical and experimental profile. The numerically simulated RMS% of about 130 is, therefore, considered representative, indicating highly non-uniform flow.

Low-porosity banked diffuser

Figure 6 depicts the downstream velocity profile for a low-porosity banked diffuser (ε = 0.73). Agreement between the numerical and experimental profile is good. The insertion of a low porosity cylinder bank has created the complete opposite flow distribution to a stalled diffuser: a jet of flow has accumulated near the diffuser side wall {0.4 < y/O < 0.5) with depleted flow velocity in the centre of the diffuser (0 < y/O < 0.4). Boundary layer separation has been prevented, but the peak velocity of the wall jet is as high as the inlet velocity U_i and flow velocity in the centre is only -20% of the inlet velocity U . The resultant flow uniformity (RMS% = 74) is better than that of an empty diffuser (RMS% = 130), but remains unsatisfactory.

Ultra-high porosity banked diffuser (optimised porosity)

Figure 7 depicts the downstream velocity profile for an ultra-high porosity banked diffuser (ε = 0.99). Close agreement is once again evident between the numerical and experimental profiles. The experimental profile exhibits slight peaks in the velocity near the centre {0 < y/O < 0.1) and near the wall (0.4 < y/O < 0.5), remnants of the core jet and wall jet, with a slight depletion of velocity in-between {0.2 < y/O < 0.3). The overall uniformity is, however, exceptionally high (RMS% 9), with all velocities in the vicinity of

30% of the inlet velocity tJ_} . Mechanisms of a banked diffuser

As mentioned above, methods of preventing boundary layer separation are broadly classified into two groups, namely those which increase fluid momentum in the boundary layer and those which reduce the adverse pressure gradient. An advantage of the banked diffuser 10 is the simultaneous incorporation of both these mechanisms, in the form of aerodynamic anisotropy and static pressure drop. Details associated with these two mechanisms are now discussed separately.

Aerodynamic Anisotropy

A cylinder bank is known to be aerodynamically anisotropic [29]: a varying level of drag is incurred depending on which direction through the cylinder bank flow passes. The aerodynamic anisotropy of the cylinder bank 12 is shown in Figure 8. The cylinder bank 12 placed within the diffuser 10 has been configured so that flow along the centreline of the diffuser, i.e. the x- axis, encounters staggered cylinders 14 and flow along the diffuser side wall 26 encounters in-line cylinders 14. The staggered arrangement incurs greater drag than the in-line arrangement, leading to a preferred flow path along the diffuser side wail 26.

Endwall flow visualisation within the low-porosity (ε = 0.73) banked diffuser demonstrates the consequences of aerodynamic anisotropy. Figure 9(a) shows the global flow distribution. Coagulated dye has accumulated in the centre of the diffuser 10 (near the x-axis), which indicates depleted flow velocity in the centre of the diffuser. Minimal dye coagulation near the diffuser side wall 26 indicates that aerodynamic anisotropy has resulted in a high-velocity wall jet, depicted by the velocity profile in Figure 6. Figure 9(b) shows the flow-field around a single cylinder 14 located near the diffuser inlet 22. For the sake of clarity, a schematic representation of Figure 9(b) is provided in Figure 9(c). Asymmetry in the shed vortices indicates higher flow velocity past the under-side of the cylinder 14, which further supports evidence of aerodynamic anisotropy and the formation of a wail jet.

Aerodynamic anisotropy results in a preferred flow path along the diffuser side wall 26, which increases near-wall fluid momentum, thereby suppressing separation.

Static Pressure Drop

An adverse pressure gradient is expected to develop inside a diffuser because a reduction in flow velocity due to the increased flow area (divergence) leads to static pressure recovery. However, the placement of the cylinder bank 12 within the diffuser 10 leads to static pressure drop, which counteracts static pressure recovery and can prevent the formation of an adverse pressure gradient.

Figure 10 exhibits the experimentally measured static pressure distribution along the diffuser side wall 26 for the three representative cylinder bank porosities. The abscissa comprises of distance along the wall (w) normalised by the length W of the diffuser side wall 26. The ordinate is the static pressure coefficient C_p defined in equation (5). The maximum experimental uncertainty of any C_p value is ± 0.02, estimated with a method reported in Holman [37].

The static pressure distribution in the empty diffuser (ε = 1.00) is almost constant along the side wall because separation of the boundary layer prevents flow expansion and static pressure recovery. The low-porosity (ε = 0.73) banked diffuser features a favourable pressure gradient along the side wall because the static pressure drop due to irreversibilities greatly exceeds static pressure recovery due to divergence. The ultra-high porosity (ε = 0.99) banked diffuser exhibits a near-neutral pressure gradient because the static pressure drop due to irreversibilities is balanced by static pressure recovery, which is the ideal scenario because the formation of an adverse pressure gradient is prevented with the least amount of energy dissipation. As a consequence, boundary layer separation is suppressed.

Summary

The cylinder bank 12 within the wide-angle diffuser 10 prevents boundary layer separation by the following two physical mechanisms:

(1) the aerodynamic anisotropy of the cylinder bank 12 encourages flow along the diffuser side wall 26 which increases near-wall fluid momentum; and

(2) static pressure drop within the cylinder bank 12 counteracts static pressure recovery, which prevents the formation of a strong adverse pressure gradient.

The efficacy of these mechanisms has been shown to depend on porosity of the cylinder bank 12 as both aerodynamic anisotropy and static pressure drop intensify with a reduction in porosity. Three porosity regimes have consequently been classified, namely excessive, deficient and critical. The porosity of the three regimes is about 1, about 0.73 and about 0.99 respectively. The fluid flow profiles in the diffuser 10 for these porosity regimes are illustrated in Figure 11(a), (b) and (c) respectively.

Referring to Figure 1(a), which shows the flow profile for the excessive porosity regime (e.g. ε = 1.00), the flow profile is characterised by boundary layer separation at the inlet to the diffuser 10 resulting in a core jet 32. The porosity is too high for either of the two suppression mechanisms to be effectual and flow uniformity is consequently very poor. In Figure 1 (b), which shows the flow profile for the deficient porosity regime (e.g. ε = 0.73), the flow profile is characterised by the prevention of boundary layer separation and the formation of wall jets 34. The porosity is low enough that both of the two suppression mechanisms are effectual and boundary layer separation is consequently prevented. However, severe aerodynamic anisotropy results in wall jets 34 that deteriorate flow uniformity and the low porosity a!so aggravates static pressure drop, in Figure 11(c), which shows the fluid flow profile for the critical porosity regime (e.g. ε = 0.99), the flow profile is characterised by highly uniform flow. Aerodynamic anisotropy and static pressure drop are sufficient to prevent boundary layer separation. However, aerodynamic anisotropy is insufficient to produce wall jets and static pressure drop is only sufficient to generate a neutral pressure gradient - not a favourable pressure gradient. The result is highly uniform flow with minimised energy dissipation.

A three-dimensional banked wide-angle diffuser

Optimisation has been successfully implemented for the two-dimensional configuration of the test diffuser 10. However, an ESP diffuser in application is typically three-dimensional because of the large area-ratio requirements. The results of the two-dimensiona! optimisation were extended to a three- dimensional design, using the principle of superpositioning.

Specifications and Characteristics

The second test diffuser 40 is a three-dimensional banked wide-angle diffuser. Again, like numerals indicate like features. From Figure 12 it can be seen that the diffuser 40 is a pyramidal diffuser. The diffuser 40 has a fluid flow section 42 which diverges in two perpendicular planes, i.e. the x-y plane and the x-z plane as indicated in Figure 12. The optima! two- dimensional configuration of the first test diffuser 10 has been superimposed onto both planes of divergence of the second test diffuser 40. The cross-sectional view of the diffuser 40, taken along its longitudinal length, is shown in Figure 13. This cross-sectional view represents both the view in the x-y plane and x-z plane. From Figure 13 it is clear that the cylinder banks in the x-y plane and x-z plane respectively is substantially identical to the cylinder bank 12 of the diffuser 10, and accordingly will not be described in detail again.

Figure 1 shows an end view of the diffuser 40 in which its cylinder bank 44 can be seen. The cylinder bank 44 is created by collapsing the two perpendicular cylinder banks of the x-y and x-z planes onto one another to form grid-like structures. The grid-like structures may seem structurally similar to conventional screens, but the mechanism of separation prevention is very different. The open-area of the grids is very high (about 80%) because separation is prevented by aligning the grid-like structures to produce aerodynamic anisotropy and by distributing grid-like structures throughout the entire diffuser 40 to reduce the adverse pressure gradient. Conversely, the open-area of conventional screens is low (40-58%) [26], because separation is prevented with an impingement effect that only requires screens at the entry and exit to the diffuser [20]. The three- dimensional design of the diffuser 40 therefore relies upon the same physical mechanisms as the two-dimensional design of the diffuser 10, namely aerodynamic anisotropy and static pressure drop. In the diffuser 40 these mechanisms are superimposed into both planes of divergence.

Detailed parameters for the pyramidal diffuser 40 used during experimental testing are listed in Table 3 below.

Table 3: Design parameters of diffuser 40

From Table 3 it can be seen that entire design of the diffuser 40 has been scaled up by an approximate factor of 2 in comparison to that of the diffuser 10. Scaling effects are not considered significant for factors less than 10 [39], but may arise for factors larger than 16 [28]. The diffuser features an overall area ratio of 10 with an included divergence angle 2Θ of 60° in both the x-y plane and x-z plane.

The pyramidal diffuser 40 has been experimentally characterised at a Reynolds number of 105, based on the hydraulic diameter of the diffuser inlet 22 and the mean stream-wise velocity measured at traverse plane A shown in Figure 13. During testing air was supplied to the test-section using a suction wind tunnei. A Pitot probe was used, in combination with a multichannel differential pressure transducer, to measure velocity profiles downstream of the diffuser 40. Fifteen velocity profiles were measured at traverse plane B shown in Figure 13. The velocity profiles were taken along the lines indicated in Figure 15.

Figure 15 shows the velocity profiles measured downstream of the pyramidal diffuser 40, plotted over one another. Local stream-wise velocities u are normalised by the mean stream-wise velocity U_t at the diffuser inlet 22. The traverse distance z is normalised by the diffuser outlet width O. The maximum experimental uncertainty of any u/O^ value is ±0.01 , estimated with a method reported in Holman [37]. The RMS% of 9 indicates highly uniform flow with no evidence of boundary layer separation or wall jets, consistent with that of the two-dimensional configuration of the test diffuser 10, confirming the applicability of the superpositioning principle.

Comparison with a screened diffuser

As mentioned above, an ESP typically utilises a screened diffuser in use. The performance of the banked diffuser 40 was compared with a conventional screened diffuser and benefits associated with the optimisation process and structural integrity of a banked diffuser will now discussed. Extensive optimisation of a screened diffuser with an identical area ratio and divergence angle 2Θ to the present banked diffuser 40 has been performed previously [26] at a similar Reynolds number (Re_Q = 8(10⁴)) to the present study (R_eQ = 10⁵). Flow uniformity and static pressure drop are compared between the banked diffuser 40 and a known screened diffuser. Flow uniformity is quantified with the RMS% definition described by equation (3) and static pressure drop is quantified with the pressure coefficient defined in equation (5) (the pressure coefficient must be evaluated at traverse plane B as shown in Figure 13 to describe the overafl static pressure drop across the entire pyramidal diffuser 40). A comparison of results is listed in Table 4 below. RMS% Overall C_p

Screened Diffuser [26] 15 -0.06

Banked diffuser 40 9 -0.23

Table 4: Comparison between screened and banked diffuser

The result of the comparison provided in Table 4 above indicate that the banked pyramidal diffuser 40 achieves a substantial improvement in flow uniformity, with a slight concession in static pressure drop. The banked diffuser 40 also presents benefits associated with design and optimisation. The optimisation procedure for a screened diffuser is complex because the number, location and open-area of the screens must all be considered for the full three-dimensional diffuser geometry. In contrast, the experimental study described above using the diffuser 10, 40 achieves exceptional flow uniformity only considering the porosity of the cylinder bank 12 for a simple two-dimensional diffuser geometry, utilising the superpositioning principle to develop the three-dimensional design.

The ultra-high porosity of the banked diffuser 10, 40 prevents clogging and ensures that sudden reductions in flow area are avoided, reducing the risk of erosion.

From the above experimental results it can be seen that boundary layer separation has been prevented in the wide-angle diffuser 0, 40 by using a specially arranged cylinder bank 12, 44 inside the diffuser. The porosity of the cylinder bank 12, 44 has been identified as a critical parameter affecting boundary layer separation and flow uniformity, and the preferred porosity of 0.99 has been found to be particularly effective. The cylinder bank 12, 44 has been shown to prevent boundary layer separation through the incorporation of two physical mechanisms, namely (1) aerodynamic anisotropy which increases fluid momentum near the wall and (2) static pressure drop which prevents the development of a strong adverse pressure gradient. The comparison with a known screened diffuser has revealed that the banked pyramidal diffuser 40 achieves superior flow uniformity. Other advantages of the banked diffuser 10, 40 include a simpler optimisation process and superior structural integrity.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to the drawings, in which like numerals indicate like features, a non-limiting example of a diffuser in accordance with a first embodiment of the invention is generally indicated by reference numeral 50. The diffuser 50 is substantially similar to the test diffuser 10 used during experimental testing and experimentation described above.

The diffuser 50 is a wide-angle diffuser and has an inlet 52 and an outlet 54. As shown in Figures 16 and 17, the inlet 52 and outlet 54 are respectively connected to rectangular conduits or ducting 56 and 58 of constant cross-section, in use, the flow of fluid through the diffuser 50 will be in a direction from an inlet 60 of the ducting 56 to an outlet 62 of the ducting 58. The length of the ducting 56 and 58 may vary between zero and any desirable length. Although the ducting 56 and 58 would typically be in the form of separate, removable sections it is envisaged that they could be integrally formed with the diffuser 50. It is further envisaged that the length of the ducting 56 and 58 could vary according to the particular requirements of the application in which the diffuser 50 is to be used. The combination of the diffuser 50 and inlet and outlet ducting 56, 58 could therefore also be referred to as a diffuser system 64. it must be understood that in the event that the inlet ducting 56 is excluded from the diffuser system 64, the inlet 52 of the diffuser 50 will act as the inlet to the diffuser system 64, Similarly, in the event that the outiet ducting 58 is excluded the outlet 54 of the diffuser 50 will act as the outlet of the diffuser system 64.

Returning to the embodiment of Figures 16 to 18, the diffuser 50 comprises a diverging flow channel located between its inlet and outlet. The channel has a number of walls, including a top wall 66.1 , a bottom wall 66.2 and two opposed sidewalls 66.3. In this first embodiment of the diffuser 50 at least a portton of the top wall 68.1 and bottom wall 68.2 respectively diverge in the fluid flow direction at a divergence angle Θ. The sidewal!s 66.3 do not diverge and are substantially in line with the sidewails of the inlet and outlet ducting 56, 58.

It is also envisaged that in an alternative embodiment of the invention only one side wall could diverge while the other side wall could carry on straight in line with the inlet ducting 56. The diffuser according to this alternative embodiment couid be described as a "half diffuser".

The diffuser 50 further includes a bank of elements located at least partially inside the flow channel so that the elements are in the fluid flow path between the inlet 52 and outlet 54. In Figures 16 to 18 the element bank and individual elements are indicated by the numerals 68 and 70 respectively.

The elements 70 are arranged such that they are staggered over at least a section, preferably the entire length of the bank 26, in a nominal stream- wise direction 72 of the flow of fluid through the diffuser 50 but are linearly aligned along at least a section, preferably the entire length, of the diverging portions of the top and bottom walls 66.1 and 66.2 of the flow channel. The arrangement of the elements 70 can clearly be seen in the detailed view of Figure 17. Form this figure it can be seen that the elements 70 are arranged in an equilateral triangle unit cell, which is repeated throughout the bank 68. The equilateral unit cell is as a result of the use of an included angle of divergence of 60 degrees. It should be understood that the angles of the unit celt are determined by the divergence angle of the diffuser as the elements 70 should always be staggered in the stream-wise direction 72 and linearly aligned along the side walls. For example, in an alternative embodiment, in which the diffuser has an included divergence angle of 70 degrees, an isosceles unit cell would be used with internal angles of 70, 55 and 55 degrees respectively. As a result of this arrangement of the elements 70, and in particular due to the aligned elements along the top and bottom walls 66.1 and 66.2 of the channel section, the boundary wall fluid momentum is, in use, increased in a direction 74 in comparison to the nominal stream-wise direction. The staggered elements 70 in the stream-wise direction 72 obstructs fluid f!ow and causes a static pressure drop through the dispersion of fluid. Due to the increase in boundary wall fluid momentum and the static pressure drop over the elements 70, boundary layer separation is reduced or substantially prevented in order to achieve substantially uniform flow velocity at the outlet 54 of the d iff user 50.

As mentioned above with respect to the experimental results, the porosity of the bank 68, i.e. the volume of the element bank unoccupied by elements 70, is critical to the efficiency of the d iff user 50 in achieving uniform fluid flow at its outlet 54. The porosity of the element bank 68 is between about 0.9 and about 0.99, preferably between about 0.950 and 0.99, and more preferably about 0.989. Although the experimentation and testing descried above only extended to a porosity of 0.989 it is envisaged that the porosity could be increased further. The upper limit of the suitable porosity range could also be defined with reference to the RMS% of the velocity profile. For example, the upper limit of the porosity range would typically be the porosity beyond which the RMS% exceeds 15.

In the first embodiment of the diffuser 50 the elements 70 are in the form of cylinders of circular cross-section which run substantially parallel to one another within the bank 68. The cylinder ends are connected to the side walls 66.3 so that their longitudinal centre axes run transversely to the stream-wise direction 72 of the fluid flow through the diffuser 50. In particular, the longitudinal centre axes of the cylinders 70 run substantially perpendicular to the stream-wise direction 72 of the fluid flow. The orientation of the cylinders 70 inside the diverging channel is clearly visible in Figure 18. Although the cylinders 70 are circular in cross-section, it is envisaged that elements of different cross-sectional shapes coufd be used. The invention is not limited to circular cylinders 70 and any other suitable cross-sectional shape could be used.

Returning to the diffuser 50, the arrangement of the individual rows of cylinders 70 is substantially similar to that of the test diffuser 10 described above and will therefore not be described again in detail.

A non-limiting example of a diffuser in accordance with a second embodiment of the invention is shown in Figures 19 to 21 and generally indicated by reference numeral 80. The diffuser 80 is substantially similar to the test diffuser 40 used during experimental testing and experimentation described above. Again, like numerals indicate like features.

The diffuser 80 is again a wide-angle diffuser comprising a diverging flow channel located between its iniet 82 and outlet 84. In this second embodiment the divergent flow channel diverges in two planes which are substantially perpendicular to each other, thereby creating a pyramidal diffuser. Similarly to the first embodtment, the channel includes a top wall 86.1 , a bottom wall 86.2 and two side walls 86.3 and 86.4. The top and bottom walls 86.1 and 86.2 form a first pair of opposing walls and the side walls 86.3 and 86.4 form a second pair of opposing walls. Each wall of each pair of opposing walls diverges at a divergence angle Θ with respect to the centre axis of the diffuser 80. The divergence angle Θ is indicated in Figure 20.

The inlet 82 and outlet 84 of the channel section are again connected to inlet ducting 88 and outlet ducting 90 as described above with reference to the first embodtment of the diffuser 50, However, in view of the fact that the channel section of the diffuser 80 diverges in two planes at the same angle Θ as described above, the ducting 88, 90 of the second embodiment are square in cross-section. Similarly to the first embodiment of the diffuser 50 the length of the ducting 88 and 90 may again vary between zero and any desirable length. The combination of the diffuser 80 and inlet and outlet ducting 88, 90 again forms a diffuser system 92.

The diffuser 90 also includes a bank of elements located at least partially inside the diverging flow channel so that the elements are in the fluid flow path between the inlet 82 and outlet 84. in Figures 19 to 21 the element bank and individual elements are indicated by the numerals 94 and 96 respectively. The elements 96 are again in the form of cylinders of circular cross-section so as to create a cylinder bank in the channel section.

Figure 20 shows a cross-section of the diffuser system 92 taken along its first plane of divergence. In view of the fact that the angle of divergence is the same in both planes of divergence, Figure 20 is also a representation of the cross-section of the diffuser system 92 taken along its second plane of divergence. From this figure it can be seen that the configuration of the cylinder bank in each individual plane of divergence is substantially similar to that of the cylinder bank 68 of the first embodiment of the diffuser 50. The cylinders 96 arranged in the first plane of divergence create a first cylinder bank while the cylinders arranged in the second plane of divergence create a second cylinder bank. Referring now to Figure 21 , it can be seen that the first and second banks of cylinders are arranged substantially perpendicular to one another so that the cylinders of the first bank run substantially perpendicularly to the cylinders of the second bank, such that the fluid flow is dispersed in both planes of divergence. In other words, the cylinders 96 in the first bank of cylinder run between the top wall 86.1 and bottom wall 86.2, while the cylinder in the second bank run between the side walls 86.3 and 86.4. The combined cylinders banks of this embodiment are indicated by the reference numeral 94.

In the second embodiment of the diffuser 80 the cylinders 96 in the different rows of the first and second cylinder banks are provided in coincidental planes so that they are collapsed onto one another to form a series of gridlike structures 98. Each grid-like structure 98 has a square outer profile when viewed in plan. As a result of the diverging channel section of the diffuser 80 the surface area of the grid-like structures 98 increases in the nominal stream-wise flow direction 72 of the fluid, i.e. from the inlet 82 to the outlet 84. it is envisaged that in an alternative embodiment not shown in the accompanying drawings the planes in which the cylinders of the first cylinder bank run may be separated in the nominal stream-wise flow direction 72 from the planes in which the cylinders of the second cylinder bank run. in this alternative embodiment there will be a gap between the first and second cylinder bank of each grid-like structure.

Returning to the diffuser 80 in accordance with the second embodiment of the invention, the porosity of each of the first and second cylinder banks in the grid-like structure 98 is again between about 0.9 and about 0.99, preferably between about 0.950 and about 0.99, and more preferably about 0.989. Accordingly, the overall porosity of the combined cylinder banks 94 is about 0.98 (0.99 * 0.99 ~ 0.98).

Similar to the diffuser 50 of the first embodiment the boundary wall fluid momentum is, in use, increased due to the arrangement of the cylinders 96. In the diffuser 80 the aligned cylinders along the top and bottom walls 86.1 and 86.2 and the aligned cylinders along the sidewalls 86.3 and 86.4 of the diverging channel section allow for an increase in boundary wall fluid momentum along ail four boundary walls of the channel section. The staggered cylinders 96 in the stream-wise direction 72 again obstruct fluid flow and cause a static pressure drop through the dispersion of fluid, in the diffuser 80 the fluid is dispersed in both planes of divergence. Boundary layer separation is again reduced or substantially prevented as a result of the increase in boundary wall fluid momentum and the static pressure drop over the cylinders 96, thereby achieving substantially uniform flow velocity at the outlet 84 of the diffuser 80.

A non-limiting example of a diffuser in accordance with a third embodiment of the invention is shown in Figures 22 to 24 and generally indicated by reference numeral 100. The inventors have identified the possibility of applying the principles of the diffusers 50 and 80 according to the first and second embodiments of the invention to a conical diffuser. The diffuser 100 is simitar to the diffusers 50 and 80 but is of conical construction. Again, like numerals indicate like features.

The diffuser 100 has a conical divergent flow channel section located between its inlet 102 and outlet 104. The side wall 106 of the conical channel section diverges at an angle Θ in ail radial directions with respect to the centre axis of the diffuser, as shown in Figure 23. It should be understood that Figure 23 shows the axisymmetric cross-section of the diffuser 100 which is revolved around the centre axis, i.e. the x-axis, to create the conical diffuser 100. It must further be understood that the conical diffuser 100 is a 360 degree revolution of the two-dimensional cross-section of the diffuser 50.

In this embodiment, the inlet 102 and outlet 104 of the diverging fluid flow channel section of the diffuser 100 are connected to cylindrical inlet and outlet ducting 108 and 110 respectively to form a diffuser system 112.

The diffuser 100 again includes a bank of elements 114 located at feast partially inside the diverging flow channel. Referring in particular to Figure 24 the element bank 114 comprises a set or series of circular elements or rings 16 of varying diameter. The set of rings are arranged about the longitudinal centre axis 1 18 of the diffuser 100. The element bank 114 includes a number of spaced apart rows of rings 116. Each row includes a number of concentric rings arranged in a common plane. Similarly to the diffusers 50 and 80, the number of rings 116 included in each row of rings increase from the inlet 102 to the outlet 104 of the diffuser 100 due to the diverging channel section. The rings 116 are held in place by fixing means, such as radially aligned runners (not shown in the accompanying drawings), for example. The concentric rings 1 16 are arranged such that the outermost rings of each row are in-line along an internal surface of the side wail 106, i.e. in the diverging direction 122 indicated in Figure 23. Again, the aligned outer rings cause fluid to be channelled along the divergent conical surface of the channel section. The rings 16 of subsequent rows are again staggered in the stream-wise direction 72 so as to disperse the fluid away from the centre axis 118. it is envisaged that boundary layer separation will again be reduced or substantially prevented as a result of an increase in boundary wall fluid momentum and a static pressure drop over the rings 116, thereby to achieve substantially uniform flow velocity at the outlet 04 of the diffuser 100. it is believed that this will be achieved by means of the same mechanisms described above with reference to diffusers 50 and 80 in accordance with the first and second embodiments of the invention.

From the above description of the diffusers 50, 80 and 100 in accordance with the invention it should be clear that the invention also concerns a method of improving the uniformity of the fluid flow velocity at an outlet of a diffuser. The method aims to achieve substantially uniform fluid flow velocity at the outlet of the diffuser by reducing boundary layer separation within the diffuser. Although the method in accordance with the invention should be apparent from the above description and the discussion on the experimental results, it is set out briefly below.

The method includes providing a diffuser 50, 80, 100 including an inlet 52, 82, 102, an outlet 54, 84, 104 and a diverging flow channel located between the inlet and outlet. A bank of elements 68, 94, 114 is provided and located in a position wherein it is at least partially inside the flow channel. In this position the eiements, which are preferably in the form of cylinders as described above, are in the fluid flow path between the inlet and outlet, in use, fluid, such as air for example, is supplied through the inlet of the diffuser in the nominal stream-wise direction 72. The cylinder bank then disperses the flow of fluid with respect to the nominal stream- wise direction in order to induce a static pressure drop across it. The arrangement of cylinders within the cylinder bank in turn allows a linear flow of fluid along the side wall of the diverging channel so as to increase fluid momentum along the boundary wall. From the above description it must be understood that the effect of the static pressure drop and the increase in fluid momentum result in the reduction of boundary layer separation to achieve substantially uniform flow velocity at an outlet of the diffuser. Preferably, the boundary layer separation is substantially eliminated by the static pressure drop and the increase in fluid momentum.

Based on the above description of the test diffusers 10, 40 and the preferred embodiments of the diffusers 50, 80 it should be understood that the arrangement of the cylinders within the cylinder bank, and in particular the porosity of the cylinder bank, plays a critical role in achieving the uniform fluid flow velocities at the outlet of the diffuser. it is worth mentioning that the experimental results achieved using the test diffusers 10, 40 have illustrated the benefits of using the diffusers in accordance with the preferred embodiments of the diffuser. It is envisaged that the same advantages as set out in the discussion of the experimental results will be achieved through the use of the diffusers 50, 80 and 100 in accordance with the three embodiments of the invention. It is believed that the diffusers 50, 80, 100 could be particularly useful in improving the efficiency of an electrostatic precipitator (ESP). However, the invention is not limited to this particular application namely and couid be used in any application we substantially uniform fluid flow velocities are desirable downstream of a diffuser. The banked diffuser 50, 80, 100 offers several advantages over known screened diffusers because superior flow uniformity is achievable with the additional benefit of a simpler design procedure. Furthermore, the ultra-high porosity bank improves robustness by inhibiting clogging and erosion. Nomenclature

A flow area

c_p static pressure coefficient

d cylinder diameter

H channel height

L length of two-dimensional diffuser 10

U length of pyramidal diffuser 40

n number of data points

0 outlet width of two-dimensional diffuser 10

0' outlet width of pyramidal diffuser 40

P static pressure

Q inlet width of two-dimensional diffuser 10

Q' inlet width of pyramidal diffuser 40

Re Reynolds number

RMS% Root Mean Square percentage

S cylinder spacing

u local stream-wise velocity

ϋ mean stream-wise velocity

Urms root mean square velocity

W distance along the diffuser wall

W diffuser side wall length

dimensionless wall distance δ* displacement thickness

ε porosity

θ divergence angle

V kinematic viscosity

P fluid density

Subscripts

1 test section inlet

2 test section outlet

i Position References

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Claims

CLAI S

1. A diffuser having an inlet and outlet, the diffuser including:

a diverging flow channel located between the iniet and outlet, the channel having a side wall of which at least a portion diverges at a divergence angle; and

a bank of element located at least partially inside the flow channel so that the elements are in the fluid flow path between the inlet and outlet, at least some of the elements being arranged such that they are staggered in a nominal stream-wise direction but are linearly aligned along the diverging portion of the side wall of the flow channel,

wherein fluid momentum along the boundary wall is, in use, increased compared to the stream-wise direction as a result of the aligned elements along the side wall of the channel and a static pressure drop is, in use, achieved through the dispersion of fluid by the staggered elements in the stream-wise direction, thereby reducing boundary layer separation to achieve substantially uniform flow velocity at an outlet of the diffuser.

2. A diffuser according to claim 1 , wherein the porosity of the bank of elements, i.e. the volume of the element bank unoccupied by elements, is between about 0.9 and about 0.99;

3. A diffuser according to claim 2, wherein the porosity of the bank of elements is about 0.989.

4. A diffuser accordtng to any one of claims 1 to 3, wherein the elements are in the form of cylinders which run substantially parallel to one another.

5. A diffuser according to claim 4, including a second bank of cylinders, wherein the diverging channel diverges in two planes which are substantially perpendicular to each other, and wherein the first and second banks of cylinders are arranged substantially perpendicular to one another so that the cylinders of the first bank run substantially perpendicularly to the cylinders of the second bank, such that the fluid flow is dispersed in both planes of divergence.

6. A diffuser according to claim 5, wherein the cylinders of the first and second cylinder banks are provided in coincidental planes so that they are collapsed onto each other to form grid-like structures.

7. A diffuser according to claim 5, wherein the planes in which the cylinders of the first cylinder bank run are separated in the stream- wise direction from the planes in which the cylinders of the second cylinder bank run.

8. A diffuser according to any one of claims 5 to 7, wherein the porosity of the bank of elements is about 0.98.

9. A diffuser according to any one of claims 1 to 3, wherein the bank of elements includes a set of concentric elements of varying diameter.

10. A diffuser according to claim 9, wherein the concentric elements are in the form of rings which are arranged such that the outermost rings are in-line with an internal surface of the diffuser and the rings are staggered in the stream-wise direction, so that flow is channelled along the diverging conical surface and dispersed away from the diffuser axis, resulting in approximately uniform flow velocity at the diffuser outlet.

11. A method of improving the uniformity of the fluid flow velocity of a diffuser including an iniet, an outlet and a diverging flow channel located between the inlet and outlet, the channel having a side wall of which at least a portion diverges at a divergence angle, the method including the following steps: providing a bank of elements located at least partially inside the flow channel so that the elements are in the fluid flow path between the inlet and outlet;

dispersing the flow of fluid with respect to a nominal stream- wise direction in order to induce a static pressure drop across the bank of elements; and

allowing linear flow of fluid along the side wall of the diverging portion of the channel to increase fluid momentum along the boundary wall;

thereby reducing boundary layer separation to achieve substantially uniform flow velocity at an outlet of the diffuser.

12. A method according to claim 11 , wherein the porosity of the bank of elements, i.e. the volume of the element bank unoccupied by elements, is between about 0.9 and about 0.99;

13. A method according to claim 12, wherein the porosity of the bank of elements is about 0.989.

14. A method according to any one of claims 11 to 13, wherein the elements are in the form of cylinders which run substantially parallel to one another.

15. A method according to claim 14, including dispersing the fluid flow in two planes of divergence by providing a second bank of cylinders, wherein the first and second banks of cylinders are arranged substantially perpendicular to one another so that the cylinders of the first banks runs substantially perpendicularly to the cylinders of the second bank.

16. A method according to claim 15, wherein the cylinders of the first and second cylinder banks are provided in coincidental planes so that they are collapsed onto each other to form grid-like structures.

17. A method according to claim 15, wherein the planes in which the cylinders of the first cylinder bank run are separated in the stream- wise direction from the pianes in which the cylinders of the second cylinder bank run.

18. A method according to any one of claims 15 to 17, wherein the porosity of the bank of elements is about 0.98.

19. A method according to any one of claims 11 to 13, wherein the bank of elements incfudes a set of concentric elements of varying diameter.

20. A method according to claim 19, wherein the concentric elements are in the form of rings which are arranged such that the outermost rings are in-line with an interna! surface of the diffuser, and the rings are staggered in the stream-wise direction, so that flow is channelled along the divergent conical surface and dispersed away from the diffuser axis, resulting in approximately uniform flow velocity at the diffuser outlet.