An apparatus for separating a multiphase fluid into a relatively light phase and a relatively heavy phase, the apparatus comprising: a separator tube which comprises a fluid inlet through which the multiphase fluid enters the apparatus, a heavy phase outlet through which the heavy phase exits the apparatus and an inner diameter surface which defines a flow bore that extends between the fluid inlet and the heavy phase outlet; a swirl element which is positioned in the flow bore downstream of the fluid inlet and which causes the multiphase fluid to rotate and separate the heavy phase from the light phase, the light phase forming an elongated core which extends axially through the flow bore radially inwardly of the heavy phase from proximate the swirl element toward the heavy phase outlet; a discharge channel through which the light phase exits the apparatus, the discharge channel being fluidly connected to a radially inner region of the flow bore; and a core stabilizer which is positioned in the flow bore between the swirl element and the heavy phase outlet and which engages the distal end of the light phase core to thereby prevent the light phase from exiting the apparatus through the heavy phase outlet even under the influence of fluctuations in the flow of the multiphase fluid through the fluid inlet; wherein the heavy phase outlet is coaxial with the separator tube and the apparatus further comprises a discharge body which is positioned coaxially within the separator tube downstream of the swirl element and upstream of the heavy phase outlet, the discharge body including a cylindrical portion which is positioned coaxially within the separator tube, a conical portion which is positioned upstream of the cylindrical portion and comprises a base that is attached to or formed integrally with an upstream end of the cylindrical portion and an outlet portion which extends transversely from the downstream end of the cylindrical portion through the separator tube, wherein the base of the conical portion comprises an outer diameter which is less than the outer diameter of the cylindrical portion to thereby define a radial shoulder which is formed between the conical portion and the cylindrical portion, wherein the core stabilizer comprises the radial shoulder; and wherein the discharge channel extends axially through the conical portion and the cylindrical portion, and wherein the conical portion comprises an upstream end which is axially spaced apart from the swirl element, an outer surface which converges radially from the base to the upstream end of the conical portion, and a discharge opening which extends axially through the upstream end of the conical portion to the discharge channel. a separator tube which comprises a fluid inlet through which the multiphase fluid enters the apparatus, a heavy phase outlet through which the heavy phase exits the apparatus and an inner diameter surface which defines a flow bore that extends between the fluid inlet and the heavy phase outlet; a swirl element which is positioned in the flow bore downstream of the fluid inlet and which causes the multiphase fluid to rotate and separate the heavy phase from the light phase, the light phase forming an elongated core which extends axially through the flow bore radially inwardly of the heavy phase from proximate the swirl element toward the heavy phase outlet; a discharge channel through which the light phase exits the apparatus, the discharge channel being fluidly connected to a radially inner region of the flow bore; and a core stabilizer which is positioned in the flow bore between the swirl element and the heavy phase outlet and which engages the distal end of the light phase core to thereby prevent the light phase from exiting the apparatus through the heavy phase outlet even under the influence of fluctuations in the flow of the multiphase fluid through the fluid inlet;