The first of your results is ok. The second one may be ok for low solid loadings because if solid distribution is more uniform then the trend that you have indicated may be obtained. Generally with increasing concentration pressure drop should increase. Please look at my paper in Wear 1998.

sir first of all thank you for ur reply...

i am also thinking the same..and i have taken bend in vertical plane and the concentration i am using is 10% , 20% and 30 % ,,,still the trend is decreasing pressure drop at particular velocity

You may also look for paper by mukhtar ahmed, SN Singh and Seshadri in International journal of multiphase flow in 1990s.

1) To the best of my knowledge, the second result is correct if the solid density is lower than liquid density in the slurry. But it is not correct if the solid density is higher than liquid density in the slurry.

2) I would like to explain you by giving an example of gas-liquid flow. You can consider gas-liquid flow from a lower point to an upper point in a vertical plane. In that situation, the pressure drop is mainly contributed by elevation change (mixture density x g x elevation change). Here, the density is mixture density of the gas-liquid flow. When the gas concentration becomes higher, the average local void fraction become higher, thus mixture density becomes smaller and smaller. Thus, the total pressure drop becomes smaller and smaller. Thus, I stated that the second result is correct if it is solid density is lower than liquid density in the slurry. You should check back the density of solid in the simulation if it is higher than liquid or not.

3) In contrast, if the solid density is higher than liquid density, the mixture density will be higher when concentration is increased. Thus, the pressure drop due to elevation change should be higher and higher with the increment of concentration.

4) However, please note that, my explanations are reasonable for long radius elbow. For short radius elbow, the frictional drops due to contraction and centrifugal acceleration are more significant than pressure drop due to elevation change. Also, there can be unexpected pressure drop in the flow can happen due to phase interaction and solid wall interaction. For very short radius elbows, in my view, the pressure drop should increase with the increment of concentration whatever the densities of phases are.

i have taken water and silica sand having density 1000 and 2650 kg/m^3 respectively..and the radius of pipe is .02 m and radius of elbow is .04 m. the size of silica particle is 425 micron, and the result is coming like above what i have stated in my status...

but when i am decreasing the particle size to 110 micron..at a particular velocity of slurry, as i increases concentration pressure drop first increases upto certain limit of 25% percentage of concentration.and after that it decreases as i increase the concentration... 

my pipe is first vertical then bend after that horizontal one....

i have done the whole problem using ansys cfd simulation s/w

Yes, Sahoo,

(1) Now I have completely understood your issue. I can only suggest that you should inspect the local volume fraction of solid particles (concnetration) in the elbow bend so that you can adjust with my explanation in previous post.

(2) I suggest you this becasue somethimes, strange and unexpectable phenomena can occur in multi-phase flows.  For example, if we simply think about the issue of increasing concentration, we may say it will increase mixture density and interaction between particles and pipe. I will increase pressure drop.

(3) On the other hand, the particles can attain larger local velocity due to buoyancy force and larger mixture velocity. It is also potential to decrease local solid fraciton at a certain condition. But the condition in No.(2) has more pobability to occur.

(4) If not, the last option is just to verify with experiments or some experimental data from literature.