COHERENT-STRUCTURE FUEL TREATMENT SYSTEMS AND METHODS

Abstract

Fuel efficiency in a combustion engine is increased by treating the fuel in a reaction chamber prior to delivering the fuel into the combustion chamber of the engine. The method includes the step of entraining a stream of exhaust gas to travel upstream through the reactor chamber in a first flow pattern. The method also includes the step of entraining a stream of fuel to travel downstream through the reactor chamber in a second flow pattern, where at least one of the first and second flow patterns comprises a structured turbulent flow.

Claims

1-16. (canceled)

17. A system for reforming a substance, comprising: a first housing; a second housing that entrains a stream of the substance and that is disposed within the first housing, wherein the second housing encloses an inner wall with surface features that are substantially large enough to be identified by naked eyes, and comprise a pattern of features selected from a group consisting of bumps, dimples, cavities, ridges, grooves, and wedges; and a connection structure that entrains the stream of the substance from a first end of the second housing to a first end of the first housing.

18. The system of claim 17, wherein the inner wall comprises coherent surface features that entrain the second stream to travel in a coherent-structured turbulence.

19. The system of claim 17, wherein an inner wall of the first housing also includes surface features that are substantially large enough to be identified by naked eyes, and comprise a pattern of features selected from the group consisting of bumps, dimples, cavities, ridges, grooves, and wedges.

20. The system of claim 19, wherein an outer wall of the second housing comprises coherent surface features that cooperates with coherent surface features on the inner wall of the first housing to entrain the first stream to travel in a coherent structured turbulence.

21. The system of claim 17, further comprises an inlet that connects to a second end of the second housing and entrains the stream of the substance into the second housing.

22. The system of claim 17, further comprising an outlet that connects to a second end of the first housing and entrains the stream of the substance out of the system.

23. The system of claim 17, further comprises a wave guide disposed in a cavity of the second housing.

24. The system of claim 23, wherein the wave guide comprises a powered electrode.

25. The system of claim 24, wherein the inner wall of the second housing comprises an electrode with opposite electrical polarity to the powered electrode of the wave guide.

26. The system of claim 23, wherein the wave guide has a shape, selected from a list consisting of a rod, an egg, a sphere, and an ellipsoid.

27. The system of claim 23, wherein the wave guide has a surface catalyst comprising an element selected from a group consisting of Fe, Ti, Ni, Pd, Pt and Cu.

28. The system of claim 17, further comprising a magnetic field producer disposed in the second housing and configured to apply a magnetic field to at least a portion of the stream of the substance within the second housing.

29. The system of claim 28, wherein the magnetic field producer comprises a stimulation coil.

31. The system of claim 17, wherein at least one of the inner and an outer wall of the second housing has a surface catalyst comprising at least one of an element selected from a group consisting of Fe, Ti, Ni, Pd, Pt and Cu.

32. The system of claim 17, further comprising an energy pickup coil configured to receive electrical energy from the stream of the substance, and an action of a wave guide disposed within the second housing.

33. The system of claim 17, further comprising an ion field generator disposed within the second housing and configured to generate ions within the stream of the substance.

34. The system of claim 17, further comprising an electric field generator disposed within the second housing and configured to apply an external electric field to at least a portion of the stream of the substance.

35. The system of claim 17, further comprising a high voltage electrode configured to ionize the substance.

36. The system of claim 17, further comprising one of a filter or a catalyst substrate disposed within the first housing.

37. The system of claim 17, wherein an enclosure of the second housing comprises pores large enough to enable at least a portion of the stream of the substance to travel from the first housing into the second housing.

38. The system of claim 17, wherein the substance comprises a liquid.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] FIG. 1 is a schematic of an engine having a pre-ignition fuel treatment system.

[0032] FIGS. 2A-2B illustrate example stimulation coils of some embodiments.

[0033] FIGS. 3A-3C illustrate example flow patterns induced by a wave guide of some embodiments.

[0034] FIG. 4 depicts an example of a pinecone arrangement of surface features and charges on a wave guide.

[0035] FIGS. 5-6 illustrate example magnetic fields induced by a wave guide of some embodiments.

[0036] FIG. 7 is a schematic of an inlet chamber having phi-based proportions.

[0037] FIG. 8 is a schematic of an ion generator of some embodiments for affecting the exhaust gas stream.

[0038] FIGS. 9A-9B are diagrams of relative counter-rotating flows of fuel and exhaust mixtures.

[0039] FIG. 10 illustrates examples of surface features of some embodiments.

DETAILED DESCRIPTION

[0040] The following discussion provides example embodiments of the inventive subject matter. Although each embodiment represents a single combination of inventive elements, the inventive subject matter is considered to include all possible combinations of the disclosed elements. Thus if one embodiment comprises elements A, B, and C, and a second embodiment comprises elements B and D, then the inventive subject matter is also considered to include other remaining combinations of A, B, C, or D, even if not explicitly disclosed.

[0041] As used herein, and unless the context dictates otherwise, the term coupled to is intended to include both direct coupling (in which two elements that are coupled to each other contact each other) and indirect coupling (in which at least one additional element is located between the two elements). Therefore, the terms coupled to and coupled with are used synonymously.

[0042] The inventive subject matter provides apparatus, systems and methods in which a fuel is being treated before ignition in a combustion engine in order to improve fuel efficiency of the engine. In one aspect of the invention, a pre-ignition fuel treatment system for an engine is presented. The system includes a reactor that passes a stream of the exhaust gas past a stream of the fuel. The reactor includes a first structure that entrains the fuel stream to travel in a first flow pattern. The reactor also includes a second structure that entrains the exhaust gas stream to travel in a second flow pattern, wherein at least one of the first and second flow patterns comprises a coherent-structured turbulence.

[0043] FIG. 1 illustrates an example of a pre-ignition fuel treatment system 100 according to an aspect of the invention. As shown, the pre-ignition fuel treatment system 100 includes a fuel tank 120, an air intake device 125, a reactor unit 130, and a combustion engine 105.

[0044] The combustion engine 105 has an intake manifold 110 and an exhaust manifold 115. In some embodiments, the combustion engine 105 is designed to combust fuel (e.g., hydrocarbon fuel such as gasoline, etc.) and air mixture that comes through the intake manifold to produce power and an exhaust gas (e.g., carbon dioxide, etc.).

[0045] The workings of a combustion engine that turns chemical energy stored within fuel and oxygen into thermal energy is well known in the art, and will not be described in detail here. In short, the engine 105 allows an amount of fuel and air (with oxygen) mixture into a combustion chamber of the engine 105 via the intake manifold 110. The engine 105 then ignites the fuel-air mixture to initiate the combustion process. The fuel and air turns into very high temperature and high pressure gas, which expands to drive the moving parts (e.g., pistons) of the engine 105. The by-products of the combustion process, such as carbon dioxide, are collectively referred to as exhaust gas. The engine 105 then releases the exhaust gas from the chamber into the exhaust manifold 115.

[0046] In FIG. 1, the fuel tank 120 and the air intake 125 are connected to the engine through the reactor unit 130. In some embodiments, the fuel from the fuel tank and air from the air intake are merged to form a fuel/air mixture before entering into the reactor unit 130. In addition, the pre-ignition fuel treatment system 100 of some embodiments includes a mechanism (not show in the figure) that converts at least some of the fuel into vapor form before mixing with the air and entering into the reactor unit 130. In some embodiments, at least 20 wt % of the fuel entering into the reactor unit 130 is in vapor form (e.g., vaporized fuel 180).

[0047] The reactor unit 130 of some embodiments is configured to treat the fuel/air mixture before sending the fuel/air mixture to the engine 105. As shown, the reactor unit 130 of some embodiments comprises a reactor housing 135 through which the stream of fuel/air mixture flows through before reaching the intake manifold 110 of the engine 105, and a wave guide 140 located within the reactor housing 135.

[0048] Studies have shown that the ionization of the fuel before combustion allows the fuel to combust more efficiently, as disclosed in U.S. Pat. No. 7,487,764 to Lee entitled Pre-ignition Fuel Treatment System, filed Aug. 10, 2007 (hereinafter Lee). Thus, according to some embodiments of the invention, the reactor unit 130 includes one or more ionization devices (not shown in the figure) for applying an ionization field to at least a portion of the fuel.

[0049] To facilitate the ionization of the fuel, the reactor unit 130 includes ionization catalysts in the reactor housing 135. Suitable catalyst elements include iron (Fe), titanium (Ti), nickel (Ni), palladium (Pd), platinum (Pt), Copper (Cu), Zinc (Zn), and Chromium (Cr). These elements under high temperature conditions become oxidized, which can act as catalysts in the ionization process. These catalysts can be placed on the surface of the wave guide 140 or along the inner wall of the reactor housing 135.

[0050] To further facilitate the ionization process, the reactor unit 130 can also include a stimulation coil (not shown in the figure) in the reactor housing 135 to apply an external ionization field to at least a portion of the fuel that passes through the reactor housing 135. In some embodiments, the stimulation coil can be placed inside of the reactor housing 135 or around the reactor housing 135.

[0051] FIG. 2A and FIG. 2B illustrate examples of suitable stimulation coil configurations. In FIG. 2A an upper coil 240 and a lower coil 250 encase the wave guide 230 in a clamshell configuration. FIG. 2B shows an embodiment that utilizes a single, toroidal stimulation coil 280 that surrounds a wave guide 260 within a reactor housing 235.

[0052] To even further facilitate the ionization process, the reactor unit 130 can include a magnetic or diamagnetic material as the core of the wave guide 140. In some embodiments, the wave guide 140 is rotatable around an axis (such as axis 175 in FIG. 1) that is parallel to the elongated length of the reactor housing 135. In these embodiments, rotational movement of the waveguide 140 generates an electromagnetic field. Additionally, as the ionized fuel molecules move around/along the wave guide, they further magnetize the wave guide 140. As the wave guide accelerates in its rotation, and its magnetic field is strengthened, the wave guide 140 further ionizes the fuel molecules.

[0053] The faster motion of the fuel molecules in turn strengthens the magnetization of the wave guide 140. Thus, the ionized fuel molecule and the wave guide 140 create a positive feedback loop that eventually drives at least some of the fuel into a plasma state. Accordingly, the reactor unit 130 turns at least some of the fuel from the liquid/vapor state into a plasma state before delivering the fuel/air mixture to the engine 105.

[0054] One purpose of this ionization process is to ionize as many fuel molecules within the reactor unit 130 as possible (and converting them into plasma state) before delivering the fuel to the engine 105. When the fuel/air mixture passes through the reactor housing 135 in a laminar flow, only a portion of the fuel molecule can be in contact with the catalyst on the wave guide 140 or the catalyst on the inner wall of the reactor housing 135. It is contemplated that entraining the fuel/air mixture stream to travel through the reactor housing 135 in a flow form that comprises a coherent-structured turbulence allows more fuel molecules to contact the catalysts on the wave guide 140 and the inner wall of the reactor housing 135. In addition, the coherent-structured turbulence flow form also forces the fuel/air mixture to be exposed to the catalysts for a longer period of time than they would otherwise if they were to travel in a laminar fashion. It has been shown that these two factors dramatically increase the ionization level of the fuel molecules.

[0055] Different embodiments provide different implementations to induce the fuel/air mixture to travel in a coherent-structured turbulence flow form. In some embodiments, the reactor unit 130 can include a wave guide 140 in a specific shape (e.g., a rod, an egg shape, a sphere, or an ellipsoid) that would induce the coherent-structured turbulence flow form. In addition, the wave guide 140 can include a pattern of features on its surface (i.e., to have a surface topology) to induce the fuel/air mixture to flow through the reactor housing in a coherent-structured turbulence flow form. Features that can be selected to be used on the wave guide's surface include, but not limited to, bumps, dimples, cavities, ridges, grooves, and wedges.

[0056] In some of these embodiments, the surface topology of the wave guide 140 is configured to induce a rotating movement within the flow form. In some embodiments, the surface topology is configured to induce micro-rotations within the flow form. Further, the surface topology can also be configured to induce vortices within the flow form. These rotating movements, micro-rotations, and vortices can add to improve the ionization of the fuel molecules.

[0057] It is also contemplated that wave guide designs that emulate biological systems (e.g. pine cones, conifer scales and bracts, seashells, etc.) can be very effective in inducing coherent-structured turbulences. Thus, in some embodiments, it is contemplated that the wave guide 140 can include scales, tiles, or horns (collectively referred to as scales) on the surface to induce structured turbulences. In some of these embodiments, the scales are disposed on the wave guide's surface in a coniferous ovulate cone pattern.

[0058] FIGS. 3A, 3B, and 3C illustrate example flow patterns induced by a wave guide 300 of some embodiments. As shown, the wave guide 300 contain scales on its surface that emulate the scales on a coniferous ovulate cone. The multiple arrows that go in and out of the scales represent example flows of a fuel/air mixture when the mixture encounters the wave guide 300. As shown, the scales on the wave guides can effectively induce rotating movements, and sometimes, micro-rotation movements as the fuel/mixture flows pass the wave guide. In some embodiments, these rotating movements and micro-rotation movements create the coherent-structured turbulence within the reactor housing 135 of the reactor unit 130. FIG. 3C shows a detailed illustration of an example flow of fuel/air mixture when the mixture passes by scale 305 and 310 of the waveguide 300.

[0059] To further facilitate the flow form of the fuel/air mixture, the inner wall of the reactor housing 135 also has a surface topology that induces the coherent-structured turbulence. In some embodiments, similar to the surface topology of the wave guide, the surface topology of the housing's inner wall also has at least one of the following features: bumps, dimples, cavities, ridges, grooves, and wedges. FIG. 10 illustrates examples of these features. In some embodiments, the surface topology of the reactor housing's inner wall and the surface topology of the wave guide are configured to complement each other to promote the coherent-structured turbulence flow form.

[0060] In some embodiments of the inventive concept, surface patterning of the rotatable wave guide can be applied to properties such as electrical charge or magnetic polarity. An example of this is shown in the lower portion of FIG. 4, which shows a wave guide 400 with a floral or pine cone pattern of positive 405 and negative 410 charges. Although a floral or pine cone pattern is illustrated, it should be appreciated that other patterns as discussed above can be suitable. Such patterning can be utilized to pattern the flow of magnetic or electric charge responsive species within a flow of fuel/air mixture. Alternatively, such patterning of electrical or magnetic properties can be utilized to enhance the modification (for example the ionization or cracking) of species within a flow of fuel/air mixture passing over the patterned surface. In some embodiments, the wave guide is rotatable

[0061] FIG. 5 illustrates an egg-shaped wave guide 500 that is also a source of a magnetic field. The arrows shown in this figure illustrate the direction of the magnetic field induced by the wave guide 500 that will help ionizing the fuel/air mixture as it passes around the wave guide 400. FIG. 6 illustrates an alternative embodiment of the egg-shaped wave guide. In this figure, the wave guide 600 includes surface pattern 605 for inducing flow patterns of the fuel/air mixture.

[0062] Referring back to FIG. 1, the reactor housing 135 has an inlet 145 coupled to the fuel tank 120 and the air intake 125 for receiving the fuel/air mixture, and an outlet 150 coupled to the intake manifold 110 of the engine 105 for sending the treated fuel/air mixture to the engine 105. In some embodiments, the inlet 145 and outlet 150 can also be configured to facilitate the induction of the coherent-structured turbulence flow form of the fuel/air mixture through the reactor unit 130.

[0063] It is contemplated that one or both of the inlet 145 and the outlet 150 have a flow form with phi-based proportions and dimensions. FIG. 7 illustrates an example reactor unit 700 having an inlet 705 and an outlet 710 with a phi-based flow form. As shown, the inlet 705 comprises a curve that conforms to a phi progression that leads the gas into the reactor chamber. It has been long observed that fluids and gasses tend to move in spirals or vortices by nature. These spirals or vortices generally conform to a mathematical progression known as the Golden Mean Ratio, or phi. These motions are well understood to be the most efficient in terms of minimizing waste energy due to friction or drag. More details about the phi progressions of fluids and gasses can be found in the International Publication Number WO2005/003616 to Harman, filed Jun. 29, 2004. The use of these forms and proportions in the inlet 145 and outlet 150 allow for 1) maximization of the thermal and kinetic energy delivered to the reactor unit 130, and 2) imparting helical motion to the gas stream, resulting in a counter-rotational relationship between the exhaust and intake gasses.

[0064] It is noted that the ionization of fuel molecules is a highly endothermic reaction, which requires a large amount of heat energy for the ionization to take place. It has been contemplated to use the heat from the exhaust gas as a heat energy source for the reactor unit 130.

[0065] Referring back to FIG. 1, the reactor unit 130 includes an exhaust housing 155. As shown, the exhaust housing 155 receives exhaust gas from the exhaust manifold 115 of the engine 105, runs the exhaust through the reactor unit 130, and release the exhaust at the other end of the exhaust housing 155.

[0066] As shown in the figure, the exhaust housing 155 of some embodiments encapsulates the reactor housing 135, such that heat from the exhaust gas can be effectively transferred to the fuel/air mixture in the reactor housing 135. To further facilitate the heat transfer from the exhaust gas to the fuel/air mixture, it is contemplated that the exhaust housing 155 of some embodiments can be configured to entrain the exhaust gas to flow in a coherent-structured turbulence flow form (e.g., a coherent dynamic flow pattern, vortices, structured rotations, rotating vortices, etc.). There are many benefits to entraining the exhaust gas to travel within the exhaust housing 155 in a coherent-structured turbulence flow form instead of a laminar form (as described in Lee). One of the benefits is that the rotation flow form forces the exhaust gas to have a longer period of exposure to the reactor housing 135 so that more heat can be transferred from the exhaust gas to the fuel/air mixture. In some studies, this flow form allows the center of the reactor housing 135 to reach a temperature of 450 degrees Celsius, when it appears that existing systems reach a considerably lower temperature.

[0067] To induce the coherent-structured turbulence, the inner wall of the exhaust housing 155 includes a pattern of features, such as bumps, dimples, cavities, ridges, grooves, and wedges, that directs the flow of the exhaust gas in a certain flow pattern. FIG. 10 illustrates examples of these features.

[0068] As shown in FIG. 1, the exhaust housing 155 has an inlet 165 that directs the exhaust gas into the exhaust housing 155 and an outlet 170 that directs the exhaust gas out of the exhaust housing 155. To further induce the exhaust gas to travel in the coherent-structured turbulence flow form and to create the counter-rotational relationship between the exhaust gas and intake gas, the inlet 165 and the outlet 170 also have flow form with phi-based proportions and dimensions that is similar to the inlet/outlet illustrated in FIG. 7.

[0069] The ionized fuel generates a magnetic field as it passes through the reactor unit 130. Similarly, the exhaust gas also generates another magnetic field as it passes through the reactor unit 130. It has been contemplated that interactions between two counter magnetic fields would enhance plasma formation in the fuel. Thus, in some of these embodiments, the exhaust housing 155 and the reactor housing 135 are configured to entrain the exhaust gas and the fuel/air mixture to rotate in opposite directions, as shown by the arrows within the exhaust housing 155 and the arrows within the reactor housing 135, to generate the counter magnetic fields.

[0070] Due to a relatively low number of positive ions in the exhaust gas, an ion generator (e.g., an electrode) can be integrated into the pre-ignition fuel treatment system 100 of some embodiments. In some embodiments, the ion generator can either protrude into the reactor chamber and/or the exhaust housing, or are flush mounted, in order to precondition and ionize both intake and exhaust gases.

[0071] FIG. 8 illustrates an example embodiment of such an ion generator. In this figure, the ion generator comprises a fuel injector 805 and high voltage electrodes 810. The fuel injector 405 injects water mist or other types of fuel into the exhaust gas stream. The electrodes turn the water molecules into ionizing charge carriers, which in turns help ionization of the exhaust gas. Both the fuel injector 805 and the high voltage electrodes 810 can be placed upstream, in the middle, and/or downstream of the reactor unit 130.

[0072] In addition to rotation movements, the exhaust housing 155 and the reactor housing 135 are configured to entrain the exhaust gas and the fuel/air mixture to travel in vortices, to further increase the interactions between the magnetic fields and the two streams. Although not shown in this figure, either the fuel/air mixture or the exhaust gas (or both) can flow in other forms of coherent-structured turbulence (e.g., vortices) in addition to the rotation.

[0073] FIGS. 9A and 9B illustrate example flow patterns for the exhaust gas and the fuel/air mixture. Specifically, FIG. 9A illustrates the rotation movements of the exhaust gas and fuel/air mixture viewed from the perspective of a cross-section of the reactor unit. In this example, the exhaust gas travels through the exhaust housing into the drawing and the fuel/air mixture travels through the reactor housing out of the drawing. As shown, the fuel/air mixture rotates within the rotation movement of the exhaust gas. In addition, the fuel/air mixture and the exhaust gas rotate in opposite directions (fuel/air mixture rotates in a counter-clockwise direction while the exhaust gas rotates in a clockwise direction).

[0074] FIG. 9B illustrates a three-dimensional simulation of how the exhaust gas and fuel/air mixture flow through the reactor unit 130. As shown, the exhaust gas rotates through the reactor unit at the outset (as shown by arrows 905) while the fuel/air mixture rotates through the reactor unit 130 in the center (as shown by arrows 910). As illustrated by this figure, at least a portion of the fuel/air mixture is induced to flow in micro vortices after passing through the reactor unit 130 (as shown by arrows 915).

[0075] It is noted that a charged particle naturally enters a magnetic field and exhibits a helical motion of left or right spin depending on its charge (i.e., positively or negatively charged). In some embodiments, inductive and capacitive coupling can be used to influence the inherent spin of the ions and electrons present in the intake and exhaust of the reactor, which sustain the particles' charge over a longer period. The high proportion of charged particles within both the fuel-air and exhaust streams facilitates the plasma reaction. In some embodiments, the helical motion of the particles is imparted by the magnetic field from the rotating wave guide, the interaction between the rotating wave guide and the fuel/air stream, and the magnetic fields generated by the external stimulation coils.

[0076] Being able to modify (enhance or diminish) the inherent instabilities within the plasma field allows tuning for a more desirable plasma reaction, leading to greater efficiencies. With an electrostatic field present, longitudinal waves create an ion cyclotron plasma instabilities and with shearing of a two-phase flow with the EGR (in the turbulent interaction of the fuel stream with the EGR), a shear flow velocity is able to create a diocotron instability, which can be seen on the surface flow of the auroras, galactic arms, and pulsars. In some embodiments, the shear flows will be complemented by the surface features of the wave guide and inner walls of the reactor.

[0077] More detailed information regarding benefits and effects from counter-rotating charged particles can be found in the following patent literatures: U.S. Pat. No. 2,991,238 to Phillips et al. entitled Pinched Plasma Reactor, filed Jun. 19, 1958; U.S. Pat. No. 6,548,752 to Pavlenko et al. entitled System and Method for Generating a Torsion Field, filed Nov. 16, 2001; and U.S. Patent Publication 2012/0223643 to Haramein entitled Plasma Flow Interaction Simulator, filed Mar. 5, 2012.

[0078] Referring back to FIG. 1, it has also been contemplated that the magnetic fields that are generated by the flow of the exhaust gas, the flow of the fuel/air mixture, and the rotation of the waveguide can be converted into power for other usage. Accordingly, in some embodiments, the reactor unit 130 also includes an energy pickup coil (not shown in the figure) that converts magnetic fields into electrical current. In some embodiments, the energy pickup coil and the stimulation coil mentioned above can be the same coil (but not necessarily).

[0079] The above examples of the embodiments describe the exhaust gas flows separately in the exhaust gas housing from the fuel/air mixture. In some embodiments, the fuel/air mixture is completely separated from the exhaust gas within the reactor unit by a barrier (e.g., the wall of the reactor housing). However, it is also contemplated that there are some benefits to have at least a portion of the exhaust gas stream to mix with a portion of the fuel/air mixture. The direct interference between the two elements allows more efficient gas exchange. Thus, in some embodiments, the reactor housing wall allows at least a portion of the exhaust gas to pass through from the exhaust housing into the reactor housing (as shown by arrow 185 in FIG. 1). In some embodiments, at least 10 wt % of the mixture within the reactor housing is derived from the exhaust gas stream.

[0080] It should be apparent to those skilled in the art that many more modifications besides those already described are possible without departing from the inventive concepts herein. The inventive subject matter, therefore, is not to be restricted except in the spirit of the appended claims. Moreover, in interpreting both the specification and the claims, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms comprises and comprising should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced. Where the specification claims refers to at least one of something selected from the group consisting of A, B, C . . . and N, the text should be interpreted as requiring only one element from the group, not A plus N, or B plus N, etc.